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Solve Linear Systems by Graphing

Goal : Solve a system of linear equations graphically

Your Notes

Systems of linear equations Two or more linear
equations in the same variables
Solution of a system of linear equations An ordered
pair that satisfies each equation in a system of
linear equations in two variables
Consistent independent system A linear system that
has exactly one solution

Example 1 Check the intersection point

Use the graph to solve the system. Then check your solution algebraically.

Equation 1
Equation 2

The lines appear to intersect at the point (2,-1).

Check Substitute 2 for x and -1 for y in each equation.

Because the ordered pair (2,-1) is a solution of each
equation, it is a solution of the linear system.


Step 1
both equations in the same coordinate
plane. For ease of graphing, you may want to
write each equation in slope - intercept form .

Step 2
Estimate the coordinates of the point of
intersection .

Step 3
Check the coordinates algebraically by
into each equation of the original
linear system.

Example 2 Use the graph-and-check method

Solve the linear system:

Equation 1
Equation 2


Step 1
both equations.

Step 2
Estimate the point of intersection. The two lines
appear to intersect at ( 2 , 3 ).

Step 3
Check whether ( 2 , 3 ) is a solution by
substituting 2 for x and 3 for y in each of
the original equations.

Equation 1 Equation 2

Because ( 2 , 3 ) is a solution of each equation in the
linear system, it is a solution of the linear system.

Guided Practice Solve the linear system by graphing.

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