Algebra 1 / Unit 6: Systems of Equations and Inequalities
6.1 Solving Systems by Graphing
Notes
A system of equations is two or more equations with the same variables. Its solution is the ordered pair that makes every equation true, which is where the graphs intersect.
- Graph both lines and read the intersection point. Check it in both equations.
- Graphing is great for seeing the answer, but exact values are easier with algebra.
Practice
Is $(2, 3)$ a solution of $y = 2x - 1$ and $x + y = 5$?
$3 = 2(2) - 1$ and $2 + 3 = 5$.
Two lines cross at $(-1, 4)$. The solution of the system is:
The intersection point is the solution.
The graphs of $y = x + 2$ and $y = -x + 6$ intersect at:
$x + 2 = -x + 6 \Rightarrow x = 2$, then $y = 4$.
Ready for more? Take the Unit 6 test.