Question

y = \frac{5}{4}x + 3\
y = \frac{1}{4}x - 1\
y = -\frac{1}{}x + 3

Explanation:

Step1: Set the equations equal

Since both equations are solved for \( y \), we can set \( \frac{5}{4}x + 3=\frac{1}{4}x - 1 \).

Step2: Subtract \( \frac{1}{4}x \) from both sides

\( \frac{5}{4}x-\frac{1}{4}x + 3=\frac{1}{4}x-\frac{1}{4}x - 1 \), which simplifies to \( \frac{4}{4}x + 3=-1 \) or \( x + 3=-1 \).

Step3: Subtract 3 from both sides

\( x + 3-3=-1 - 3 \), so \( x=-4 \).

Step4: Substitute \( x = - 4 \) into one of the equations

Let's use \( y=\frac{1}{4}x - 1 \). Substitute \( x=-4 \): \( y=\frac{1}{4}(-4)-1=-1 - 1=-2 \).

Answer:

The solution to the system of equations is \( x = - 4 \) and \( y=-2 \), so the point of intersection is \( (-4,-2) \).