algebra 1 (grades 8-9)...completing the corresponding questions on the 4.2.1 study: slope-intercept...

Algebra 1 (Grades 8-9)

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CHARLES COUNTY PUBLIC SCHOOLS

Algebra 1 (Grades 8-9) Mathematics

Weeks 7-8 (May 18 – May 29)

Dear parents,

If your child is participating in distance learning solely through the completion of our instructional packets, you are required to call or email the principal to inform them of your child’s participation status, since packet-assignments will not be collected until a later time. Please keep all of your child’s work in a safe place until you are notified of when, where and how to submit. Thank you for your attention to this matter.


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Estimados padres, Si su hijo/a está participando en el aprendizaje a distancia completando solamente nuestros paquetes de instrucción, deberá llamar o enviar un correo electrónico al director para informarle sobre el estado de participación de su hijo/a, ya que las asignaciones realizadas en los paquetes no se recopilarán hasta más tarde. Por favor mantenga todo el trabajo de su hijo/a en un lugar seguro hasta que se le notifique cuándo, dónde y cómo presentarlo. Gracias por su atención a este asunto.


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Student: _________________________________ School: _____________________________

Teacher: _________________________________ Block/Period: ________________________

Packet Directions for Students Week 7:

Read through the Instruction and examples on Slope-Intercept Equation of a Line while completing the corresponding questions on the 4.2.1 Study: Slope-Intercept Equation of a Line Study Guide.

Complete 4.2.1 Study: Slope-Intercept Equation of a Line Study Guide. o Check and revise solutions using the 4.2.1 Study: Slope-Intercept Equation of a

Line Study Guide Answer Key

Complete Quiz Slope-Intercept Equation of a Line

Week 8:

Read through the Instruction and examples on Two Variable Systems: Elimination while completing the corresponding questions on the 5.3.1 Study: Two Variable Systems: Elimination study guide.

Complete 5.3.1 Study: Two Variable Systems study guide. o Check and revise solutions using the 5.3.1 Study: Two Variable Systems:

Elimination study guide Answer Key

Complete Quiz Two Variable Systems Elimination


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Slope-Intercept Equation of a Line

In this section, you will learn more about how the properties of a line are related to its

equation. Before you begin, make sure to read the objectives below, which show what you will

cover as you learn how to work with the slope-intercept equation of a line.

Objectives

Write and graph equations in the form y = mx + b.

Understand that the graph of a linear equation in the form y = mx + b shows the set of

all of its solutions plotted in the coordinate plane.

Using function notation, evaluate a linear function for inputs in its domain.

Graph an equation representing a real-world linear relationship, and identify the

meaning of the slope and y-intercept.

Compare the slopes and y-intercepts of linear functions represented in different ways.

Slope-Intercept Equation of a Line

If you know the slope and y-intercept of a line, you can find the slope-intercept equation for the

line.

y = mx + b

m is the slope of the line.

b is the y-coordinate of the y-intercept

Problem 1:

Slope = 7

y-intercept = (0, 8)

The values from the given slope and y-intercept join the "y = x +" to form the equation.

y = 7x + 8

Problem 2:

Slope = 5

y-intercept = (0, 3)

The values from the given slope and y-intercept join the "y = x +" to form the equation.

y = 5x + 3


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Graphing the Slope-Intercept Equation

The equation of the line has a slope of and a y-intercept of (0, 5).

The graph of the equation is the set of all its solutions plotted in the coordinate plane,

making a line.

Slope

As you might have figured out, the slope of the line is the coefficient of the variable x in the equation.

This is true for all lines — not just those that pass through the origin (as you might have noticed in an

earlier section).

What is the slope of the line that passes through (0, 5) and (10, 0)?

0−5

10−0= −

1

2

Where Is the y-Intercept?

Since the line goes through the point (0,5) the y-intercept is 5

So what is the Equation of the Line?

𝑦 = 𝑚𝑥 + 𝑏

𝑦 = −1

2𝑥 + 5


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Evaluate a Linear Function

You can evaluate a slope-intercept equation for different input values.

For example, the function notation for y = 2x + 3 is f(x) = 2x + 3.

If f(x) = 2x + 3, what is f(–2)?

Substitute -2 for x in the function

𝑓(𝑥) = 2(−2) + 3 = −4 + 3 = −1

So when x = -2, f(x) = -1

This means the point (-2, -1) is a solution to the function and (-2, -1) is on the line y = 2x + 3

Checking Other Solutions

Point 1:

This is the point (–1, 1).

f(–1) = 2(–1) + 3 = 1

Point 2:

This is the y-intercept (0, 3).

f(0) = 2(0) + 3 = 3

Point 3:

This is the point (1, 5).

f(1) = 2(1) + 3 = 5

Find the Slope and y-Intercept

You can find the y-intercept and slope of a line from a graph.

To find the slope, identify two points on the line

and set up the fraction 𝑚 =𝑅𝑖𝑠𝑒

𝑟𝑢𝑛=

𝑢𝑝 2

𝑟𝑖𝑔ℎ𝑡 6=

2

6=

1

3

To find the y-intercept, look for the point where

the graph crosses the y-axis… when 𝑦 = 4

So the equation of the line is 𝑦 =1

3𝑥 + 4


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Practice — Find the Slope and y-Intercept

Time to practice! Try to answer the three questions below.

1) What is the b-value for this graph?

b = -3

2) What is the slope of this graph?

Slope is −2

1= −2

3) What is the slope-intercept equation of this graph?

𝑦 = −2𝑥 − 3


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Graph the Line

If you know the slope and the y-intercept of a line, you can draw or identify its graph.

Start by graphing the y-intercept, and then use the slope (rise/run) to locate and graph a few other

points.

Example: Graph a line that has a slope of and passes through (0, –4).

Step 1: Plot the given point.

Graph the point (0, –4), which is also the y-intercept.

Step 2: Use the slope to plot a second point.

Identify the rise and run using the slope formula.

The rise is 3 and the run is 2.

From (0, –4), move up 3 units (rise) and to the right 2 units (run) to arrive at the point (2, –1).

Step 3: Use the slope to plot a third point.

Plot a third point as a check.

For example, from (2, –1), a line segment extends upward by 3 points (rise), and a second to the right by

2 points (run). This leads to the new point (4, 2).

Step 4: Connect the points with a straight line.

Use a straightedge to draw a line that connects the three points:

(0, –4), (2, –1), and (4, 2)


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Comparing Linear Functions

You can compare the slopes and y-intercepts of functions that are shown in different ways.

Example:

g(x) = 4x – 5

This is the graph of f(x):

Use the equation of g(x) and the graph of f(x) to compare the slopes and y-intercepts.

For g(x) the slope is 4 and the y-intercept is -5

For f(x) the slope is -4 and the y-intercept is 2

Real-World Linear Functions

The temperature in Frostville is d (degrees Fahrenheit) at midnight, when h = 0.

d = –2h + 10

Here, h is the number of hours after midnight.

What is the graph of d?

.


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Interpreting the Temperature Problem

Starting at midnight (h = 0) in Frostville, the temperature d (degrees Fahrenheit)

is d = –2h +10 where h is the number of hours after midnight.

1) What is the meaning of the y-intercept in terms of the problem?

2) What is the meaning of the slope in terms of the problem?

The temperature is dropping 2 degrees every hour

Write a Real-World Linear Equation

It costs $25.00 to rent a moving van, plus an additional $0.50 for every mile you drive.

1) If c(x) represents the cost in dollars, and x represents the miles you drive, what is the equation

for c(x)?

c(x) = 0.50x + 25

2) What is the graph of c(x)?

3) What is the meaning of the slope and y-intercept?

It costs $25.00 to rent a moving van, plus an additional $0.50 for every mile you drive. The cost function

is c(x) = 0.50x + 25

4) How much does it cost to rent the van if you drive 80 miles?

C(80) = .5(80) + 25 = 40 = 25 = 65

$65

At midnight, when h = 0, the temperature was 10 degrees.


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Interpret the Slope and y-Intercept

Penny was given money to start a college fund. She put the money in the bank. Every month after that,

she deposits the same amount of money.

The amount in the bank is modeled by y = 800 + 25x, where y is the amount of money in the bank

and x is the number of deposits.

What does the y-intercept mean in this situation?

Penny was given $800 to start her college fund.

What does the slope mean in terms of the problem?

Penny puts $25 in her account every month.

More Examples:

Find the equation of the straight line that has slope m = 4 and passes through the point (–1, –6).

Okay, they've given me the value of the slope; in this case, m = 4. Also, in giving me a point on the line,

they have given me an x-value and a y-value for this line: x = –1 and y = –6.

In the slope-intercept form of a straight line, I have y, m, x, and b. They've given me the value for m,

along with values for an x and a y. So the only thing I don't have so far is a value for is b (which gives me

the y-intercept). Then all I need to do is plug in what they gave me for the slope and the x and y from

this particular point, and then solve for b:

y = mx + b

(–6) = (4)(–1) + b

–6 = –4 + b

–2 = b

Then the line equation must be "y = 4x – 2".

https://www.purplemath.com/modules/solvelin.htm


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What if they don't give you the slope?

Find the equation of the line that passes through the points (–2, 4) and (1, 2).

Well, if I have two points on a straight line, I can always find the slope; that's what the slope formula is

for.

𝑚 =2 − 4

1 − −2=

−2

3= −

2

3

Now I have the slope and two points. I know I can find the equation (by solving first for "b") if I have a

point and the slope; that's what I did in the previous example. Here, I have two points, which I used to

find the slope. Now I need to pick one of the points (it doesn't matter which one), and use it to solve

for b.

Using the point (–2, 4), I get:

y = mx + b

4 = (– 2/3)(–2) + b

4 = 4/3 + b

4 – 4/3 = b 12/3 – 4/3 = b

b = 8/3

...so y = ( – 2/3 ) x + 8/3.

https://www.purplemath.com/modules/slope.htm


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4.2.1 Study: Slope-Intercept Equation of a Line

Name:

Date:

Use the questions below to keep track of key concepts from this lesson's study activity.

Key Terms

In your own words, write a definition for each key term listed below.

slope-intercept equation:

y-axis:

y-intercept:

1) Practice: Accessing Prior Knowledge

In your own words, write brief definitions for the terms slope and y-intercept.

slope:

y-intercept:

2) Practice: Using Visual Cues

Complete the labels for this equation. Write slope or y-intercept in each blank.

3) Practice: Organizing Information

Fill in the blanks in this sentence.

The graph of the equation y = mx + b is a _______ that shows ____________________ to the equation.


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4) Practice: Making Inferences

Answer each question.

1. Does every line have a slope and a y-intercept? Explain.

2. What is the greatest number of y-intercepts a line can have? Explain.

5) Practice: Using Visual Cues

Write the missing number in the equation for each line.

y = ___x + 1 y = ___x – 1

y = 3x + ___ y = x + ___


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Fill in the missing information in each chart.


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4.2.1 Study: Slope-Intercept Equation of a Line

ANSWER KEY

Key Terms


slope-intercept equation:

One way to write the equation of a line. It is shown as y = mx + b, where m is the slope and b is the y-

coordinate of the line's y-intercept.

y-axis:

The vertical axis in a Cartesian coordinate system.

y-intercept:

A point where the graph of a function crosses the y-axis. A function has at most one y-intercept. The y-

intercept of the line with equation y = mx + b is the point (0, b).

1) Practice: Accessing Prior Knowledge

In your own words, write brief definitions for the terms slope and y-intercept.

slope:

(Page 1) the steepness of a line

y-intercept:

(Page 6) the point where the graph of a line crosses the y-axis

2) Practice: Using Visual Cues (Page 1)

Complete the labels for this equation. Write slope or y-intercept in each blank.

3) Practice: Organizing Information (Page 2)

Fill in the blanks in this sentence.

The graph of the equation y = mx + b is a line that shows the set of all solutions to the equation.


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4) Practice: Making Inferences (Page 5)

1. Does every line have a slope and a y-intercept? Explain.

Possible response: No; most vertical lines have neither.

2. What is the greatest number of y-intercepts a line can have? Explain.

Possible response: One, because a line extends forever in both directions, so once a line has crossed

the y-axis, it will never cross it again.

Another possible response: A vertical line that runs through the y-axis will have infinite y-intercepts. But

this line is not a linear function.

5) Practice: Using Visual Cues (Pages 3 and 4)

Write the missing number in the equation for each line.

y = 2x + 1 y = x – 1


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y = 3x + 1 y = x + −3

6) Practice: Organizing Information (Pages 1 – 7)

Fill in the missing information in each chart.


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Quiz: Slope-Intercept Equation of a Line

Question 1

1a ) The graph of y = –3x + 4 is:

A. a line that shows only one solution to the equation.

B. a point that shows one solution to the equation.

C. a point that shows the y-intercept.

D. a line that shows the set of all solutions to the equation.

Question 2

2a ) What is the y-intercept of the line given by the equation below?

y = 8x + 7

A. (7, 0)

B. (0, 8)

C. (0, 7)

D. (8, 0)


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Question 3

3a ) On a piece of paper, graph y = –2x – 3. Then determine which answer matches the graph you drew.

A.

B.

C.

D.


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Question 4

4a ) What is the slope-intercept equation of the line below?

A. y = 3x + 4

B. y = –3x – 4

C. y = 3x – 4

D. y = –3x + 4


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Question 5

5a ) The function f(x) is shown in this graph.

The function g(x) = –6x – 5.

Compare the slopes.

A. The slope of f(x) is undefined and the slope of g(x) is

negative.

B. The slope of f(x) is greater than the slope of g(x).

C. The slope of f(x) is less than the slope of g(x).

D. The slope of f(x) is the same as the slope of g(x).


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Question 6

6a ) The temperature, t, in Burrtown starts at 21°F at midnight, when h = 0. For the next few hours, the

temperature drops 4 degrees every hour.

Which equation represents the temperature, t, at hour h?

A. t = –21h + 4

B. t = 4h + 21

C. t = 21h + 4

D. t = –4h + 21


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Question 7

7a )The cost, c(x), for a taxi ride is given by c(x) = 2x + 3.00, where x is the number of minutes.

On a piece of paper, graph c(x) = 2x + 3.00. Then determine which answer matches the graph you drew,

including the correct axis labels.

A.

B.

C.

D.


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Question 8

8a ) The cost, c(x), for a taxi ride is given by c(x) = 2x + 3.00, where x is the number of minutes. What

does the slope mean for this situation?

A. The rate of change of the cost of the taxi ride is $2.00 per

minute.

B. The taxi ride costs a total of $3.00.

C. The taxi ride costs $2.00 per trip.

D. The rate of change of the cost of the taxi ride is $3.00 per

minute.

Question 9

9a )Mario was given some birthday money. He puts the money in an account. Every month after that, he

deposits the same amount of money.

The equation that models this situation is y = 75x + 50, where y is the amount of money in the account

and x is the number of deposits.

What does the y-intercept mean in this situation?

A. He puts $75 in the account each month.

B. He was given $50 for his birthday.

C. He puts $50 in the account each month.

D. He was given $75 for his birthday.


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Question 10

10a ) If f(x) = 4x – 12, what is f(2)?

A. 4

B. 8

C. –4

D. –20


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Two-Variable Systems: Elimination

Graphing and substitution are very important methods for solving two-variable systems. However, you'll

find that when you can choose how to solve two-variable systems, you'll usually use elimination.

Eliminating variables makes systems easier to solve.

The elimination method will also give you plenty of practice with adding, subtracting, and multiplying

variables.

First, though, make sure to read the objectives you'll cover in this lesson.

Objectives

Identify when to use elimination instead of graphing or substitution to solve systems of

equations.

Learn how to add or subtract the same value on both sides of an equation to eliminate terms.

Manipulate equations in standard form using multiplication to create equal or opposite

coefficients.

Solve systems of equations using the elimination method.

Prove that performing operations such as multiplication and addition on a system of equations

produces a system with the same solution.

Solve a system of equations with infinite solutions algebraically and graphically.

Two-Variable Systems: Elimination

Sometimes it is hard to solve a system of linear equations using the substitution method or graphing.

Take a look at these equations:

15x + 7y = 4

5x + 7y = –3

It would be hard to graph these equations, and it would take a lot of math to isolate the variable.

For problems like this one, there is a method called elimination. You'll learn about the elimination

method in this study.

Adding Equal Amounts

The big idea in the elimination method is that an equation stays equal, or balanced, if you add (or

subtract) the same amount on each side.

After the addition or subtraction, the equation is still balanced, or true.


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Math Examples

Now take a look at a couple of math examples.

Each example shows that you can add or subtract the same amount on both sides of an equation and

the equation will stay equal.

Example #1

2x – y = 10

y = 3

The y from the bottom equation moves up and is added to the left side of the top equation, and the 3

from the bottom equation moves up and is added to the right side of the top equation.

2x – y + y = 10 + 3

The left side of the equation becomes 2x and the right side of the equation becomes 13.

2x = 13

Example #2

3x + 2y = 17

3x = 5

The 3x from the bottom equation moves up and is subtracted from the left side of the top equation

(after the 3x), and the 5 from the bottom equation moves up and is subtracted from the right side of the

top equation.

3x – 3x + 2y = 17 – 5

The left side of the equation becomes 2y and the right side of the equation becomes 12.

2y = 12

Example #1 Example #2

Since y = 3, we can add y to one side

of the equation and add 3 to the

other side and the equation stays

equal.

Since 3x = 5, we can subtract 3x from

one side of the equation and subtract 5

from the other side and the equation

stays equal


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Adding Equations to Eliminate a Variable

In each math example, we were able to eliminate a variable from the top equation. That left us with one

variable in the top equation, just as with substitution.

Remember, we are adding or subtracting two equal things on each side of an equation, so we are

correctly using the rules of algebra.

Add the equations to eliminate the x–term.

39 = 19y

Example Problem

Take a look at the problem below. What could you do to eliminate the y-term from one of

the equations?

15x + 7y = 4

5x + 7y = 2

Subtract the equations

After you eliminate the y-term, you have a one-variable equation that you know how to solve.

15x + 7y = 4

– (5x + 7y = 2)

10x + 0y = 2

Find x and enter it below as a fraction in lowest terms.

10x = 2

x = 1/2


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Solving for y

On the previous page, you found the value of x. The next step is to solve for y. The elimination method

involves two steps:

1. Use elimination to find the value of one variable.

2. Use substitution to find the value of the other variable.

Now you can use the x-value to solve for y.

Substitute the value for x into one of the equations, as you did with the substitution method.

Click one of the equations to substitute

The equation moves underneath to the left and then the is substituted in for the x


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Check the Answer

Now you can check that the solution is correct by substituting the values into both of the equations.

Practice — Eliminating a Variable

Solve the System of Linear Equations: Step 1

What do you get if you subtract the bottom equation from the top equation?

4x = 8


Solve 4x = 8 for x.

x = 2


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Substitute x = 2 into either equation and solve for y.

y = –4

Solve the System of Linear Equations: The Solution

Write this solution as an ordered pair.

(2, -4)

Ex 1Solve the system of equations. Enter your answer as an ordered pair.

4x + 5y = 14

–4x – 2y = –8

(1, 2)

Solve the system of equations. Enter your answer as an ordered pair.

5x + 5y = 20

–5x + 4y = 7

(1, 3)


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Standard Form

You may have noticed that the elimination method works best if the equations are in standard

form: ax + by = c.

y = 4x – 1

y – 5 = 2x

Step 1:

Start with the top equation.

Subtract 4x from both sides of the top equation.

y – 4x = 4x – 1 – 4x

y – 4x = –1

Step 2:

Rewrite the terms so the x-term is first.

The top equation is now in standard form.

y – 4x = 4x – 1 – 4x

y – 4x = –1

–4x + y = –1

Step 3:

Now work with the bottom equation.

Subtract 2x from both sides of the bottom equation.

y – 4x = 4x – 1 – 4x

y – 4x = –1

–4x + y = –1

y – 5 – 2x = 2x – 2x

y – 5 – 2x = 0

Step 4:

Rewrite the terms in the bottom equation so the x-term is first.

y – 4x = 4x – 1 – 4x

y – 4x = –1

–4x + y = –1

y – 5 – 2x = 2x – 2x

y – 5 – 2x = 0

–2x + y – 5 = 0

Step 5:

Add 5 to both sides of the bottom equation.


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The bottom equation is now in standard form.

y – 4x = 4x – 1 – 4x

y – 4x = –1

–4x + y = –1

y – 5 – 2x = 2x – 2x

y – 5 – 2x = 0

–2x + y – 5 + 5 = 0 + 5

–2x + y = 5

Step 6:

The system of equations is in standard form.

y – 4x = 4x – 1 – 4x

y – 4x = –1

–4x + y = –1

y – 5 – 2x = 2x – 2x

y – 5 – 2x = 0

–2x + y – 5 + 5 = 0 + 5

–2x + y = 5

Creating Equal or Opposite Coefficients

The elimination method works best if one variable has equal or opposite coefficients. Then you can just

add or subtract.

What do you do if none of the variable terms have equal or opposite coefficients?

In the example below, notice that 6 is a multiple of 3: 3 • 2 = 6.

So, if you multiply each side of the top equation by 2, the x-terms will have equal coefficients.

HYPERLINK "javascript:void(0)"


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Check the Answer

As always, you should check that your solution is correct. This time, let's substitute the values

for x and y back into the original equations.

Another Example

Infinitely Many Solutions

The problem from the previous page had an infinite number of solutions, so the lines must lie one on

top of the other.

If we put the equations in slope-intercept equation form, we can see that they have the same slope and

the same y-intercept.

t


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One More Example

You can't always multiply just one equation to get terms with equal or opposite coefficients. Sometimes,

you need to multiply each equation by a different number, as in the example here.

The coefficients of the x-terms have a common multiple of 10.

Multiply the top equation by 5 and the bottom equation by 2 to create equations that have x-terms with

coefficients of 10.

The x-coefficients are highlighted and shown to switch so that the top equation is multiplied by the

bottom coefficient and the bottom equation is multiplied by the top coefficient.

"10x" and "8y" are subtracted from the left and "32" is subtracted from the right


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Deciding Which Variable to Eliminate

When you have a system of linear equations and none of the terms match, you can choose which term

you want to eliminate.

Example #1

To make the x-terms match, you can multiply the first equation by 3 and the second equation by 2.

The x-coefficients are shown to switch so that the top equation is multiplied by the bottom x-coefficient

and the bottom equation is multiplied by the top x-coefficient.

Example #2

To make the y-terms match, you can multiply the first equation by –5 and the second equation by 4.

The y-coefficients are shown to switch so that the top equation is multiplied by the bottom y-coefficient

and the bottom equation is multiplied by the top y-coefficient.


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5.3.1 Study: Two-Variable Systems: Elimination

Name:

Date:

Use the questions below to keep track of key concepts from this lesson's study activity.

Key Terms


elimination:


Fill in the blanks.

Fill in the blanks to complete the flowchart.

2) How to Use Elimination to Solve a System of Two Linear Equations


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3) Practice: Summarizing

Fill in the blanks to complete each rule.

Rule Example

If the variables have coefficients, use

subtraction to eliminate the terms.

If the variables have coefficients, use

addition to eliminate the terms.


Answer the questions and complete the steps to solve the system of equations below.

A. Which variable will you eliminate? Explain your choice.

B. Add the two equations.

C. Solve the equation for x. Show your work.

D. Substitute that value for x into either equation and solve for y. Show your work.

E. Write your solution as an ordered pair (x, y).

F. Use substitution to check your solution for the system. Show your work.


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Fill in the blanks.

The first step in solving this system of linear equations is to multiply both sides of the bottom equation

by 2.

5x + 2y = 14

3x – y = 4

This works because of the__________________________.

The next step is to add the two equations together.

This works because of the__________________________.



A. How can you get equal coefficients for the x-terms?

B. Multiply the top equation by 2.

C. Subtract the bottom equation from the new top equation. Show your work.

D. Use substitution to solve the system for x. Show your work.




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5.3.1 Study: Two-Variable Systems: Elimination

ANSWER KEY

Key Terms


elimination:

The adding or subtracting of two equations to remove one of the variables. Elimination is a step in

solving a system of equations.


Fill in the blanks.


Fill in the blanks to complete the flowchart.

How to Use Elimination to Solve a System of Two Linear Equations


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3) Practice: Summarizing (Pages 1 – 8)

Fill in the blanks to complete each rule.

Rule Example

If the variables have equal coefficients, use subtraction

to eliminate the terms.

If the variables have opposite coefficients, use addition

to eliminate the terms.



A. Which variable will you eliminate? Explain your choice.

y

Possible explanation: Because it has opposite coefficients

B. Add the two equations.

19x = 57

C. Solve the equation for x. Show your work.

Answer:

D. Substitute that value for x into either equation and solve for y. Show your work.

Answer:


(3, 4)


Answer:


43


Fill in the blanks.

The first step in solving this system of linear equations is to multiply both sides of the bottom equation

by 2.

5x + 2y = 14

3x – y = 4

This works because of the__________________________. multiplication property of equality

The next step is to add the two equations together.

This works because of the__________________________. addition property of equality



A. How can you get equal coefficients for the x-terms?

Multiply both sides of the top equation by 2.

B. Multiply the top equation by 2.

6x + 4y = 24

C. Subtract the bottom equation from the new top equation. Show your work.

Answer:

D. Use substitution to solve the system for x. Show your work.

Answer:


(2, 3)


Answer:


44

Quiz: Two-Variable Systems: Elimination Question 1

1a ) Add the equations.

A. 4y = 28

B. 2y = 26

C. 6x – 4y = –28

D. –2y = –28

Question 2

2a ) Subtract the equations.

A. –10x = 28

B. 10x = 28

C. 2y = 22

D. 6y = 28


45

Question 3

3a ) Use the elimination method to solve the system of equations. Choose the correct ordered pair.

2x + 4y = 16

2x – 4y = 0

A. (2, –4)

B. (4, 2)

C. (2, 4)

D. (4, –2)

Question 4


3x + 5y = 48

–3x + 5y = 12

A. (–3, 5)

B. (6, 6)

C. (16, 0)

D. (–4, 0)


46

Question 5


7x + 4y = 39

2x + 4y = 14

A. (3, 4)

B. (3, 2)

C. (5, 1)

D. (5, 4)

Question 6

6a ) Solve the system of equations and choose the correct ordered pair.

3x + 2y = 12

6x + 3y = 21

A. (2, 3)

B. (4, 3)

C. (4, 0)

D. (3, 2)


47

Question 7


3x + 5y = 2

9x + 11y = 14

A. (4, –2)

B. (3, 2)

C. (3, –2)

D. (4, 2)

Question 8


3x – 4y = 26

2x + 8y = –36

A. (6, 2)

B. (2, 5)

C. (2, –5)

D. (6, –2)


48

Question 9


3x + 4y = 38

5x – 5y = –30

A. (2, 8)

B. (3, 4)

C. (2, 6)

D. (3, 9)

Question 10

10a ) To begin solving this system of linear equations by elimination, you can add the equations.

This step works because of the _____.

A. multiplication property of equality

B. distributive property

C. commutative property

D. addition property of equality

algebra 1 (grades 8-9)...completing the corresponding questions on the 4.2.1 study: slope-intercept...

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