Question

think about the process which point on the graph is the solution of the system of equations? use the graph to determine the solution of the system of equations.
$y = -3x + 8$
$y + 4 = 2(x - 4)$
which point on the graph is the solution of the system of equations?
a. the point where the lines intersect the y - axis
b. the point where the lines intersect the origin
c. the point where the lines intersect the x - axis
d. the point where the lines intersect each other
what is the solution of the system of equations?
(type an ordered pair.)

Explanation:

Step1: Simplify the second equation

$y + 4 = 2(x - 4)$
$y + 4 = 2x - 8$
$y = 2x - 12$

Step2: Set equations equal (solve for $x$)

Set $-3x + 8 = 2x - 12$
$-3x - 2x = -12 - 8$
$-5x = -20$
$x = \frac{-20}{-5} = 4$

Step3: Substitute $x=4$ to find $y$

Substitute $x=4$ into $y = -3x + 8$
$y = -3(4) + 8 = -12 + 8 = -4$

Answer:

D. The point where the lines intersect each other
$(4, -4)$