Question

1. $y = 3x - 4$ and $y = -\frac{1}{2}x + 10$

Explanation:

Step1: Set the equations equal

Since \( y = 3x - 4 \) and \( y = -\frac{1}{2}x + 10 \), we set \( 3x - 4 = -\frac{1}{2}x + 10 \).

Step2: Solve for \( x \)

Add \( \frac{1}{2}x \) to both sides: \( 3x + \frac{1}{2}x - 4 = 10 \). Combine like terms: \( \frac{6}{2}x + \frac{1}{2}x = \frac{7}{2}x \), so \( \frac{7}{2}x - 4 = 10 \). Add 4 to both sides: \( \frac{7}{2}x = 14 \). Multiply both sides by \( \frac{2}{7} \): \( x = 14 \times \frac{2}{7} = 4 \).

Step3: Find \( y \)

Substitute \( x = 4 \) into \( y = 3x - 4 \): \( y = 3(4) - 4 = 12 - 4 = 8 \).

Step4: Check

Substitute \( x = 4 \), \( y = 8 \) into \( y = -\frac{1}{2}x + 10 \): \( 8 = -\frac{1}{2}(4) + 10 = -2 + 10 = 8 \). It works.

Answer:

\((4, 8)\)