Section 7.1

Solving Linear Systems by Graphing

A System is two linear equations:

• Ax + By = C• Dx + Ey = F

• A Solution of a system of linear equations in two variables is and ordered pair (x, y) that ___________ each equation in the system.

• When graphing both equations for the linear system, you are looking for the ___________ of the linear equations.

Where A, B, C, and D are integers and x & y are variables

satisfy

Solution

Checking the intersection point

• Use the graph to solve the system of linear equations. Then check your solution algebraically.

3 7x y 3x3x

3 7y x

4 2 6x y 4x

2 4 6y x 2 3y x

4x

2, 1

Rules for Solving a linear system using graphing and check

1) Write each equation in slope intercept form (y=mx + b)

2) Graph both equations thoroughly (neatness counts)

3) Estimate the coordinates of the point of intersection

4) Check the coordinates algebraically by substituting into each equation of the original linear system.

1x y xx

1y x

1y x

3x y x x

3y x

1,2

4 8x y xx

4 8y x

12

4y x

7x y x x

7y x

4, 3

3 5x y 3x3x

3 5y x

3 5y x

3 1x y 3x 3x

3 1y x

1,2

3 4 4x y 3x 3x

4 3 4y x

31

4y x

3

34

y x

NO SOLUTION!!!!!!!!!!!!!!!!

𝟔 𝒙+𝟖 𝒚=𝟐𝟒−6 𝑥 −6 𝑥

8 𝑦=−6 𝑥+24