Question

1. what is a solution to the system $y = x + 2$ and $y = -x + 6$?

a. $(4,2)$
b. $(4,8)$
c. $(1,3)$
d. $(2,4)$

Explanation:

Step1: Set equations equal

$x + 2 = -x + 6$

Step2: Solve for x

$2x = 4 \implies x = 2$

Step3: Find y via substitution

$y = 2 + 2 = 4$

Step4: Verify with second equation

$y = -2 + 6 = 4$

Answer:

d. (2,4)