Solving Systems by Graphing
Solve systems of linear equations by graphing in Grade 9 algebra: convert each equation to slope-intercept form, graph on the same axes, and read the intersection point as the solution.
Key Concepts
Property The solution of a system of linear equations can be found by graphing the equations on the same coordinate plane. The solution is the point of intersection. Explanation Time for some treasure hunting! Graph both lines and find the spot where they cross paths. That single point, the 'X' on the map, is the solution that works for both equations at the same time. Examples To solve the system $y = x + 3$ and $y = 2x + 1$, graph both lines. They intersect at the point $(2, 5)$, which is the solution. To check, $5 = 2 + 3$ and $5 = 2(2) + 1$ are both true.
Common Questions
What are the steps to solve a system by graphing?
Convert both equations to slope-intercept form (y = mx + b). Graph each line on the same coordinate plane using slope and y-intercept. Identify the point where the lines intersect — that point is the solution (x, y).
What are the three possible outcomes when solving systems by graphing?
One intersection point: one unique solution. Parallel lines (never intersect): no solution (inconsistent system). Same line overlapping: infinitely many solutions (dependent system).
How do you verify an intersection point is the correct solution?
Substitute both x and y coordinates into BOTH original equations. If both equations are true, the intersection point is the solution. If either equation fails, recheck your graphs for errors.