Question

solve the following system of equations graphically on the set of axes below.
$y = x - 7$
$y = -dfrac{3}{2}x - 2$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intersection by solving equations

Set \(x - 7=-\frac{3}{2}x - 2\).
Add \(\frac{3}{2}x\) to both sides: \(x+\frac{3}{2}x - 7=- 2\).
Combine like terms: \(\frac{2x + 3x}{2}-7=-2\) → \(\frac{5x}{2}-7=-2\).
Add 7 to both sides: \(\frac{5x}{2}=5\).
Multiply both sides by \(\frac{2}{5}\): \(x = 2\).

Step2: Find y - value

Substitute \(x = 2\) into \(y=x - 7\): \(y=2 - 7=-5\).

Answer:

The solution is \(x = 2\), \(y=-5\) (the intersection point is \((2,-5)\)).