Solving System by Graphing

Pre-Algebra · Axiom Academy

EXAMPLE Solving Systems by Graphing Graph two lines, read off where they cross, then confirm the solution algebraically. Solve the system y = 2x + 1 and y = -x + 4 by graphing. Find the point (x, y) that makes both equations true, then verify it algebraically. Nice work. You solved a linear system by graphing, then confirmed it with algebra. The recipe: Tabulate, then plot: pick a few x-values, compute y for each equation, and plot the points to draw each line. Read the intersection: where the two lines cross is the one (x, y) that satisfies both equations at once. Confirm with algebra: set the right-hand sides equal, solve for x , then substitute to get y . Result: the lines meet at (1, 3) , and (1, 3) checks out in both y = 2x + 1 and y = -x + 4 . Graphing gives you a picture of the solution; the algebra makes it exact. Together they tell you the system has exactly one solution — the point where the lines cross.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.