Goal : Solve a system of linear equations
graphically
Your Notes
Example 1 Check the intersection point
Use the graph to solve the system . Then check your
solution algebraically.
 |
Equation 1 |
 |
Equation 2 |
Solution
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.
SOLVING A LINEAR SYSTEM USING THE GRAPHAND- CHECK
METHOD
Step 1
Graph 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
substituting into each equation of the original
linear system.
Example 2 Use the graph-and- check method
Solve the linear system:
 |
Equation 1 |
 |
Equation 2 |
Solution
Step 1
Graph 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.
