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) \\)\\( dots \\)which point on the graph is the solution of the system of equations?\\( \bigcirc \\) a. the point where the lines intersect the y - axis\\( \bigcirc \\) b. the point where the lines intersect the origin\\( \bigcirc \\) c. the point where the lines intersect the x - axis\\( \bigcirc \\) d. the point where the lines intersect each other

Explanation:

Step1: Identify solution definition

The solution to a system of linear equations graphed is the point that satisfies both equations, which is where the two lines cross.

Step2: Match to option

Among the choices, option D describes this intersection point of the lines.

Step3: Verify via solving equations

First, rewrite the second equation in slope-intercept form:
$y + 4 = 2(x - 4)$
$y = 2x - 8 - 4$
$y = 2x - 12$
Set equal to first equation:
$-3x + 8 = 2x - 12$
$-3x - 2x = -12 - 8$
$-5x = -20$
$x = 4$
Substitute $x=4$ into $y=-3x+8$:
$y = -3(4) + 8 = -12 + 8 = -4$
The intersection point is $(4, -4)$, which is where the lines cross each other, confirming option D is correct.

Answer:

D. The point where the lines intersect each other
The solution to the system is $\boldsymbol{(4, -4)}$