Question

9.
y = -\frac{1}{4}x + 3
y = -2x - 4

Explanation:

Step1: Set equations equal

Since \( y = -\frac{1}{4}x + 3 \) and \( y = -2x - 4 \), set \( -\frac{1}{4}x + 3 = -2x - 4 \).

Step2: Solve for x

Add \( 2x \) to both sides: \( 2x - \frac{1}{4}x + 3 = -4 \).
Combine like terms: \( \frac{8}{4}x - \frac{1}{4}x + 3 = -4 \) → \( \frac{7}{4}x + 3 = -4 \).
Subtract 3: \( \frac{7}{4}x = -7 \).
Multiply by \( \frac{4}{7} \): \( x = -7 \times \frac{4}{7} = -4 \).

Step3: Find y

Substitute \( x = -4 \) into \( y = -2x - 4 \): \( y = -2(-4) - 4 = 8 - 4 = 4 \).

Answer:

The solution is \( x = -4 \), \( y = 4 \) (or the point \((-4, 4)\)).