Download Solving Linear Systems Using the Graphing Method

Solving Linear Systems Using
the Graphing Method
Definition A linear system of equations is a set of two (or more)
linear equations containing the same variables.
A solution to a linear system is a point (a, b) that satisfies
all the equations in the system.
Remark 1 Here is an example of a linear system.
x+y =6
−x + y = 2
A solution to this system is a point that satisfies both equations in the
system. From earlier topics we know that all the points satisfying the
top equation form a line. Similarly, all the points satisfying the bottom
equation form a line. So, the solution to this system must be the point
at the intersection of these two lines!!! As shown below, the solution to
this system is (2, 4).
Main Idea To solve a linear system by graphing:
On the same grid carefully graph each equation (using the
slope and y-intercept). The intersection of the two lines will be
the solution to the system.
Remark 2 Be careful! Solving systems by graphing is imprecise. To make sure
you have the correct solution point, check your proposed solution point
in both equations.
Example 1 Solve the linear system by graphing.
2x − y = 4
4x + y = 2
Example 2 Solve the linear system by graphing.
x + 2y = 4
2x + 4y = 12
Example 3 Solve the linear system by graphing.
x + 2y = 4
2x + 4y = 8