Example Card: Solving a System by Graphing
Solve systems of two equations by graphing in Grade 9 algebra: graph both lines on one coordinate plane, find their intersection visually, and confirm the solution satisfies both original equations.
Key Concepts
But what if you aren't given a point? Let's find the intersection ourselves by graphing. This second key idea, solving a system by graphing, is a visual way to find the one point that works for both equations.
Example Problem.
Solve the system by graphing: $2x + y = 8$ and $x y = 1$.
Common Questions
How do you graph a system of equations to find the solution?
Convert each equation to slope-intercept form (y = mx + b). Plot the y-intercept, then use the slope to find additional points. Draw both lines on the same axes and mark the intersection point as the solution.
What should you do if you cannot find a point of intersection by graphing?
If the lines appear parallel (same slope, different y-intercepts), there is no solution. If they look identical (same line), there are infinitely many solutions. For non-integer intersections, use algebraic methods for exact answers.
How do you verify a graphically found solution (2, 5) for a system?
Substitute x = 2 and y = 5 into BOTH equations separately. Both equations must produce true statements. If one fails, either the graphing was inaccurate or an arithmetic error occurred during verification.