Example 1

The equations «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mn»3«/mn»«/math» and «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mo»-«/mo»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«/math» are a linear system. Determine the solution to the system by graphing. Verify the solution.

Step 1: Graph the system.

Step 2: Determine the solution to the system.

The two lines intersect at (-2,-1), so this is a solution to the system.

Step 3: Verify the solution by substitution.

 The solution must be verified for each equation in the system, separately.

The solution satisfies each equation. The solution is verified.