Solving by Graphing

Algebra 1 · Axiom Academy

Find where two lines meet by graphing them and reading off the intersection point. Solve the system of linear equations by graphing: y = 2x + 1 and y = -x + 4 . Find the point (x, y) that satisfies both equations at once. Both lines plotted on one coordinate plane. The solution is the single point where they cross. Nice work — you solved a system of equations by graphing. The process: Graph the first line: use its slope and y-intercept to plot y = 2x + 1 . Graph the second line: on the same plane, plot y = -x + 4 . Find the intersection: the single point where the lines cross is the solution. Verify: substitute the intersection's x and y back into both equations to confirm they hold. The solution is (1, 3) — graphing turns "solve the system" into "find where the lines meet."

This is the written version of the interactive lesson above. See the full Algebra 1 course.