Question

solve the following system of equations graphically on the set of axes below.
$y = x - 4$
$y = -dfrac{1}{2}x - 7$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intersection by solving equations

Set \( x - 4=-\frac{1}{2}x - 7 \).
Add \( \frac{1}{2}x \) to both sides: \( x+\frac{1}{2}x - 4= - 7 \).
Combine like terms: \( \frac{3}{2}x - 4= - 7 \).
Add 4 to both sides: \( \frac{3}{2}x= - 3 \).
Multiply both sides by \( \frac{2}{3} \): \( x = - 2 \).

Step2: Find y - value

Substitute \( x = - 2 \) into \( y=x - 4 \): \( y=-2 - 4=-6 \).

Answer:

The solution is \( x = - 2 \), \( y = - 6 \) (the point of intersection is \((-2,-6)\)).