Question

solve the following system of equations graphically on the set of axes below.
$y = x - 7$
$y = -dfrac{1}{3}x - 3$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intersection by solving equations

Set \( x - 7 = -\frac{1}{3}x - 3 \).
Add \( \frac{1}{3}x \) to both sides: \( x + \frac{1}{3}x - 7 = -3 \).
Combine like terms: \( \frac{4}{3}x - 7 = -3 \).
Add 7 to both sides: \( \frac{4}{3}x = 4 \).
Multiply both sides by \( \frac{3}{4} \): \( x = 3 \).

Step2: Find y - value

Substitute \( x = 3 \) into \( y = x - 7 \): \( y = 3 - 7 = -4 \).

Answer:

The solution is \( (3, -4) \) (the point of intersection of the two lines \( y = x - 7 \) and \( y = -\frac{1}{3}x - 3 \)).