Question

1. $y = \frac{5}{4}x$

$y = \frac{-3}{4}x + 8$

Explanation:

Step1: Set the two equations equal

Since \( y = \frac{5}{4}x \) and \( y = \frac{-3}{4}x + 8 \), we set \( \frac{5}{4}x=\frac{-3}{4}x + 8 \).

Step2: Solve for \( x \)

Add \( \frac{3}{4}x \) to both sides: \( \frac{5}{4}x+\frac{3}{4}x=\frac{-3}{4}x+\frac{3}{4}x + 8 \), which simplifies to \( \frac{8}{4}x=8 \), or \( 2x = 8 \). Then divide both sides by 2: \( x=\frac{8}{2}=4 \).

Step3: Find \( y \)

Substitute \( x = 4 \) into \( y=\frac{5}{4}x \): \( y=\frac{5}{4}\times4 = 5 \).

Answer:

The solution to the system of equations is \( x = 4 \) and \( y = 5 \), so the point of intersection is \( (4,5) \).