Algebra

7.1 Solving Linear Systems by Graphing

System of Linear Equations(linear systems) Two equations with two variables.

An example: 4x + 5y = 32x = 6y -10

A solution to a linear system is an ordered pair (x, y) that, when substituted in, makes both equations true.

Thus, the solution would be on both graphs.

The solution(s) is the intersection of the lines.

Is the ordered pair a solution to the system of equations? Yes or no. -2x + y = -11 (6, 1) -x – 9y = 15Plug it in and check!-2(6) + (1) = -11?-12 + 1 = -11?-11 = -11 Yes.

-(6) – 9(1) = 15?-6 – 9 = 15?-15 = 15? No.

The point is not a solution to the system of equations.

Use the graph to find the solution to the system of equations. Then check your solution algebraically.

y = 3x -12

y = -2x + 3

The solution seems to

be (3, -3). Check this

solution algebraically on your

paper. Who can

check it on the board?

Yes. The point is a solution

to the system.

Steps to “Graphing to Solve a Linear System”

1) Write each equation in a form that is easy to graph (Slope-int or standard)

2) Graph both equations on the same coordinate plane

3) Find the point of intersection

4) Check the point algebraically in the system of equations

Solve the system graphically. Check the solution algebraically. 3x – 4y = 12 -x + 5y = -26

Step 1) Put the equations in a graph-able form.3x – 4y = 12 Find the x-int. and y-int.

3(0) – 4y = 12 -4y = 12 y = -3 The y-int is (0, -3) Graph it!

3x – 4(0) = 12 3x = 12 x = 4 The x-int is (4, 0) Graph it!

Put -x + 5y = -26 into slope-int form. +x +x 5y = x – 26 y = 1/5 x – 5 1/5

The solution to the system seems to be (-4, -6)

..

. .

Check (-4, -6) in the system algebraically.

3x - 4y = 12 (-4, -6) -x + 5y = -26

3(-4) - 4(-6) = 12?-12 + 24 = 12?12 = 12 Yes.

-(-4) + 5(-6) = -26?4 – 30 = -26?-26 = -26 Yes.

The point is a solution to the system of equations.

You try! Solve the system graphically. Check the solution algebraically. 3x + y = 11 x - 2y = 6

Step 1) Put the equations in a graph-able form.3x + y = 11 Put into slope-int form.

-3x -3x y = -3x + 11 Graph it!

x - 2y = 6 Put into slope-int form. -x -x -2y = -x + 6 y = 1/2 x – 3 Graph it!

The solution to the system seems to be (4, -1)

..

. .

.

Check (4, -1) in the system algebraically.

6x + 2y = 22 (4, -1) x - 2y = 6

6(4) + 2(-1) = 22?24 - 2 = 22?22 = 22 Yes.

(4) - 2(-1) = 6?4 + 2 = 6?6 = 6 Yes.

The point is a solution to the system of equations.

HW

P. 401-403 #11-19 Odd, 25-33 Odd, 47-59 Odd