Solving Linear Systems by Graphing

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4 3 2 1 0

In addition to level 3.0 and above and beyond what was taught in class,  the student may:· Make connection with other concepts in math· Make connection with other content areas.

The student will write, solve and graph systems of equations and inequalities. - Solve systems of linear equations graphically, with substitution and with elimination method. - Solve systems that have no solutions or many solutions and understand what those solutions mean. - Find where linear and quadratic functions intersect. - Use systems of equations or inequalities to solve real world problems.

The student will be able to: - Solve a system graphically. - With help the student will be able to solve a system algebraically.

With help from theteacher, the student haspartial success with solving a system of linear equations and inequalities.

Even with help, the student has no success understanding the concept of systems of equations.

Focus 5 Learning Goal – (HS.A-CED.A.3, HS.A-REI.C.5, HS.A-REI.C.6, HS.A-

REI.D.11, HS.A-REI.D.12): Students will write, solve and graph linear systems of equations and inequalities.

•With an equation, any point on the line (x, y) is called a solution to the equation.

•With two or more equations, any point that is true for both equations is also a solution to the system.

Is (2,-1) a solution to the system?

3x + 2y = 4

-x + 3y = -5

1. Check by graphing each equation. Do they cross at

(2,-1)?

2. Plug the (x,y) values in and see if both equations are

true.3(2) + 2(-1) = 4

6 + (-2) = 4

4 = 4

-2 + 3(-1) = -5

-2 + (-3) = -5

-5 = -5

Helpful to rewrite the equations in slope-intercept form.

y = -3/2x +2y = 1/3x – 5/3

Now graph and see where they intersect. Do they cross at (2,-1) ?

SOLVE -Graph and give solution then check

(plug solution into each equation)

y = x + 1

y = -x + 5

Solution (2, 3)

Solve: If in standard form, rewrite in slope-intercept form, graph the lines, then plug in to check.

2x + y = 4

y = -2x + 4

y= x - 2Y

X2-2

y = x + (-2)

y = -2x + 4

x – y = 2

Solution: (2,0)

Check

2x + y = 4 x – y = 22(2) +0 = 4 2 – 0 = 2 4 =4 2 = 2

Both equations work with the same solution, so (2,0) is the solution to the system.

Example 1:If you invest $9,000 at

5% and 6% interest, and you earn $510 in

total interest, how much did you invest

in each account?Equation #1 .05x + .06y = 510Equation #2 x + y = 9,000

Solve by graphing (find the x, y-intercepts)

When x = 0 When y = 0

.06y = 510

y = 8,500 x + y = 9,000

y = 9,000

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.05x = 510

x = 10,200 x + y =

9,000 x = 9,000

Thousands at 5%

Tho

usan

ds a

t 6%

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(3,000, 6,000) Solution

Investment

Graph is upper right quadrant, crossing at

(3,000, 6,000)

Answer: $3,000 is invested at 5% and $6,000 is invested at 6%

CHECK ANSWER TO MAKE SURE!!