Question

solve the system of linear equations below.

$y = -2x + 19$
$y = x + 7$

a. $x = 4, y = 11$
b. $x = -12, y = -5$
c. $x = -4, y = 3$
d. $x = 8, y = 3$

Explanation:

Step1: Set equations equal

Since both equal \( y \), set \( -2x + 19 = x + 7 \).

Step2: Solve for \( x \)

Subtract \( x \) and 19: \( -3x = -12 \), so \( x = 4 \).

Step3: Find \( y \)

Substitute \( x = 4 \) into \( y = x + 7 \): \( y = 4 + 7 = 11 \).

Answer:

A. \( x = 4 \), \( y = 11 \)