Solve the system by graphing.EXAMPLESolve the system by graphing: Strategy We will graph b...

Solve the system by graphing.

EXAMPLE

Solve the system by graphing:

Strategy We will graph both equations on the same coordinate system.

WHY The graph of a linear equation is a picture of its solutions. If both equations are graphed on the same coordinate system, we can see whether they have any common solutions.

Solution

Although infinitely many ordered pairs (x, y)satisfy x + 2y = 4, and infinitely many ordered pairs (x, y)satisfy 2x − y = 3, only the coordinates of the point where the graphs intersect satisfy both equations. From the graph, it appears that the intersection point has coordinates (2, 1). To verify that it is the solution, we substitute 2 for x and 1 for y in both equations and verify that (2, 1) satisfies each one, as shown below.

Check:

Since (2, 1) makes both equations true, it is the solution of the system.