Question

question
solve the system of equations graphed on the coordinate axes below.
$y = \frac{1}{2}x + 2$
$y = -3x - 5$

Explanation:

Step1: Set the equations equal

Since both equations equal \( y \), set \( \frac{1}{2}x + 2 = -3x - 5 \).

Step2: Solve for \( x \)

Add \( 3x \) to both sides: \( \frac{1}{2}x + 3x + 2 = -5 \). Combine like terms: \( \frac{7}{2}x + 2 = -5 \). Subtract 2: \( \frac{7}{2}x = -7 \). Multiply by \( \frac{2}{7} \): \( x = -2 \).

Step3: Find \( y \)

Substitute \( x = -2 \) into \( y = \frac{1}{2}x + 2 \): \( y = \frac{1}{2}(-2) + 2 = -1 + 2 = 1 \).

Answer:

The solution is \( x = -2 \), \( y = 1 \) (or the ordered pair \( (-2, 1) \))