SWBAT… Solve a system of equations using the graphing method Tues, 2/5

Agenda1. WU (5 min)2. Notes (15 min)3. Graphing method posters (30 min)

Warm-Up:

Set-up your notes – Topic is “System of Equations – Graphing Method”

HW#1: Systems - Graphing

We are starting a new unit: System of Linear Equations & Inequalities

SWBAT…1. Solve a system of linear equations using the graphing method

2. Solve a system of linear equations using the substitution method

3. Solve a system of linear equations using the elimination method (adding, subtracting, or multiplying)

4. Write and solve a system of equations based on real life scenarios (application word problems)

5. Solve a system of linear inequalities using the graphing method

(~4 week unit)

What should I already know to be successful in this unit (pre-requisite skills)?

1. Distributive property

2. Combining like terms

3. Solving a multi-step equation

4. Solving a literal equation

5. Finding the slope and y-intercept of lines

6. Graphing lines (solving for y)

7. Writing equations of lines in slope-intercept form

8. Writing and finding ordered pairs

9. Parallel lines and intersecting lines

MT = Math Tutoring

T = Tuesday

Th = Thursday

R206 = Room 206

R208 = Room 208

MT = T + Th + R206 + R208

System of Equations: Graphing Method

What is a system of equations? A collection of equations involving the same

set of variables. We will be dealing with two equations and two

variables.

x – y = 2

3y + 2x = 9

Step 1) Write the equations of the lines in slope intercept form.

Step 2) Graph each line on the same graph.

Step 3) Determine the point of intersection and write this point as an ordered pair.

• If the two equations have no points in common, the system of equations has no solution.

• Parallel lines; same m and different b

• If the two equations represent the same line, the system of equations has infinitely many solutions.

• Same line; same m and same b

Step 4) If there is one solution, check your work. Substitute the ordered pair for x and y in each equation.

Graph the system of equations. Determine whether the system has one solution, no solution, or infinitely many solutions. If the system has one solution, determine the solution and check your answer.

x – y = 2

3y + 2x = 9Step 1: Write each equation in slope-intercept form.

x – y = 2

-x -x

-y = -x + 2

y = x – 2

3y + 2x = 9

-2x -2x3y = -2x + 93 3 3

y x 2

33

-1 -1 -1

x

y Step 2: Graph each line on the same graph

Step 3: Determine the point of intersection.

(3,1).

This system of equations has one solution, the point (3, 1).

y = x – 2

y x 2

33

Step 4: Check your answer 3 – 1 = 2 3(1) + 2(3) = 9

2 = 2 3 + 6 = 9 9 = 9

Activity-System of equations – Graphing Method You and a partner will be given a system of

equations to graph on poster board

Directions:1. Solve the system using the graphing method

(show work on poster)

2. Determine the number of solutions it has

3. If the system has one solution, name it

4. If the system has one solution, check your answer

SWBAT… Solve a system of equations using the graphing method Wed, 2/6

Agenda

1. WU (15 min)

2. Conclusions about graphing method and solutions (25 min)

3. Review HW#1 (10 min)

Warm-Up:

What are advantages and disadvantages to the graphing method.

Advantage to graphing?

Graphing clearly shows whether a system of equations has one solution, no solution, or infinitely many solutions.

It’s visual!

Disadvantage to graphing?

Finding the exact values of x and y from a graph can be difficult.

Compare slope (m) and the y-intercept ( b)

Types of lines

Picture /Diagram

Number of solutions

Compare slope (m) and the y-intercept ( b)

Types of lines

Picture /Diagram

Number of solutions

 

One solution

     

     

Compare slope (m) and the y-intercept ( b)

Types of lines

Picture /Diagram

Number of solutions

Different slope (m) Same or different y-intercept (b)

Intersecting lines

 

One solution

     

     

Compare slope (m) and the y-intercept ( b)

Types of lines

Picture /Diagram

Number of solutions

Different slope (m) Same or different y-intercept (b)

Intersecting lines

 

One solution

     No Solution

     

Compare slope (m) and the y-intercept ( b)

Types of lines

Picture /Diagram

Number of solutions

Different slope (m) Same or different y-intercept (b)

Intersecting lines

 

One solution

Same slope (m) Different y-intercept (b) 

Parallel lines  

No Solution

     

Compare slope (m) and the y-intercept ( b)

Types of lines

Picture /Diagram

Number of solutions

Different slope (m) Same or different y-intercept (b)

Intersecting lines

 

One solution

Same slope (m) Different y-intercept (b) 

Parallel lines  

No Solution

     

Infinite Solutions

Compare slope (m) and the y-intercept ( b)

Types of lines

Picture /Diagram

Number of solutions

Different slope (m) Same or different y-intercept (b)

Intersecting lines

 

One solution

Same slope (m) butDifferent y-intercept (b) 

Parallel lines  

No Solution

 Same slope (m) andSame y-intercept (b)

 

Same lines 

Infinite Solutions

Graph the system of equations. Determine whether the system has one solution, no solution, or infinitely many solutions. If the system has one solution, determine the solution.

1 3 3

3 9 9

.

x y

x y

23

54

5 3

. y x

y x

3 3

2 6

. x y

x y

x

yThe two equations in slope-intercept form are:

y x

y x

3

2 6

This system of equations has one solution, the point (3,0).

The point of intersection of the two lines is the point (3, 0).

Lines Intersect

The two equations in slope-intercept form are:

x

y

y x

y x

3

54

3

5

This system of equations represents two parallel lines.

This system of equations has no solution because these two lines have no points in common.

Lines Do Not Intersect Parallel Lines

x

yThe two equations in slope-intercept form are:

y x

y x o r y x

1

31

3

9

9

9

1

31

These two equations represent the same line.

Therefore, this system of equations has infinitely many solutions.

Lines that are the Same

HW#1: Systems-Graphing Method Answers:

1. 1 Solution: (1, 2)

2. 1 Solution: (-4, -2)

3. Infinite Solutions

4. 1 Solution: (-2, -2)

5. Solution

6. No Solution

Exit Slip

y – 2x = 6

-4y – 4x = 12

1. Find the solution to the below system of equations using the graphing method.

(Hint: Write each equation in slope-intercept form)

1. How many solutions exist? Write the solution as an ordered pair.

2. Check your answer.