Question

which point is a solution to the system of linear equations?
$y = -x + 4$
$x - 3y = 12$
(0, 3)
(1, 2)
(6, -2)
(4, -4)

Explanation:

Step1: Substitute $y=-x+4$ into second equation

Substitute $y = -x + 4$ into $x - 3y = 12$:
$x - 3(-x + 4) = 12$

Step2: Simplify and solve for $x$

Expand and combine like terms:
$x + 3x - 12 = 12$
$4x = 24$
$x = 6$

Step3: Find $y$ using $x=6$

Substitute $x=6$ into $y=-x+4$:
$y = -6 + 4 = -2$

Step4: Verify the solution

Check $(6,-2)$ in $x-3y=12$:
$6 - 3(-2) = 6 + 6 = 12$, which matches.

Answer:

C. (6, -2)