Question

solve the following system of equations graphically on the set of axes below.
$y = -\frac{3}{2}x - 2$
$y = \frac{1}{2}x + 6$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intersection by solving equations

Set the two equations equal: $-\frac{3}{2}x - 2=\frac{1}{2}x + 6$
Add $\frac{3}{2}x$ to both sides: $-2 = \frac{1}{2}x+\frac{3}{2}x + 6$
Simplify: $-2 = 2x + 6$
Subtract 6: $-8 = 2x$
Divide by 2: $x = -4$

Step2: Substitute x to find y

Use $y=\frac{1}{2}x + 6$, substitute $x=-4$:
$y=\frac{1}{2}(-4)+6=-2 + 6 = 4$

Answer:

The solution is $x = -4$, $y = 4$ (the point $(-4, 4)$ is the intersection of the two lines).