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 = -2x + 2 )
( y + 4 = 2(x - 3) )
which point on the graph is the solution of the system of equations?
a. the point where the lines intersect the x - axis
b. the point where the lines intersect the origin
c. the point where the lines intersect the y - axis
d. the point where the lines intersect each other

Explanation:

Step1: Rewrite second equation

$y + 4 = 2(x - 3)$ simplifies to $y = 2x - 10$

Step2: Set equations equal

$-2x + 2 = 2x - 10$

Step3: Solve for x

$-2x -2x = -10 -2$
$-4x = -12$
$x = 3$

Step4: Find y value

Substitute $x=3$ into $y=-2x+2$:
$y = -2(3) + 2 = -4$

Step5: Identify solution type

The solution $(3, -4)$ is where the two lines intersect.

Answer:

D. The point where the lines intersect each other