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Solving by Graphing
Solve the system using the graphing method.
Step 1 — Graph the first equation. Rewrite in slope-intercept form by isolating :
The slope is and the y-intercept is (0, 7). Plot the y-intercept and use the slope to find additional points, then draw the line.
Step 2 — Graph the second equation on the same grid. For , use the intercept method. Setting gives , so the x-intercept is (6, 0). Setting gives , so and the y-intercept is . Plot these intercepts and draw the line.
Step 3 — Determine the relationship between the lines. The two lines intersect at a single point.
Step 4 — Identify and verify the solution. The lines intersect at . Check this ordered pair in both equations:
- First equation: . Since is true, the first equation is satisfied.
- Second equation: . Since is true, the second equation is also satisfied.
Because makes both equations true, the solution of the system is .
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