Question

1. y = -x + 4

y = (5/3)x - 4

Explanation:

Step1: Set equations equal

To find the intersection (solution) of \( y = -x + 4 \) and \( y=\frac{5}{3}x - 4 \), set them equal:
\( -x + 4=\frac{5}{3}x - 4 \)

Step2: Solve for \( x \)

Add \( x \) to both sides:
\( 4=\frac{5}{3}x + x - 4 \)
Combine like terms (\( x=\frac{3}{3}x \)):
\( 4=\frac{8}{3}x - 4 \)
Add 4 to both sides:
\( 8=\frac{8}{3}x \)
Multiply both sides by \( \frac{3}{8} \):
\( x = 3 \)

Step3: Find \( y \)

Substitute \( x = 3 \) into \( y = -x + 4 \):
\( y=-3 + 4=1 \)

Answer:

The solution (intersection point) is \( (3, 1) \)