Question

what is the solution to the system of equations?
$y = x + 3$
$y = -x + 1$
a. $(-1, 2)$
b. $(2, -1)$
c. $(1, 2)$
d. $(2, 1)$

Explanation:

Step1: Set equations equal

Since the solution to a system of linear equations is the point of intersection, we set \( y = x + 3 \) and \( y = -x + 1 \) equal:
\( x + 3 = -x + 1 \)

Step2: Solve for \( x \)

Add \( x \) to both sides:
\( 2x + 3 = 1 \)
Subtract 3 from both sides:
\( 2x = -2 \)
Divide by 2:
\( x = -1 \)

Step3: Find \( y \)

Substitute \( x = -1 \) into \( y = x + 3 \):
\( y = -1 + 3 = 2 \)

Answer:

A. \((-1, 2)\)