Question

100 points! asap! Which graph best represents the solution to the system of equations shown below?

y = -2x + 14
y = 2x + 2

A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8.
A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair 8, 3.
A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 8, negative 3.
A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 3, 8.

Answer 1

Answer:

A)  A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair (3, 8)

Step-by-step explanation:

Given equations:

$\textsf{Equation 1}: \quad y=-2x+14$

$\textsf{Equation 2}: \quad y=2x+2$

Substitute Equation 2 into Equation 1 and solve for $x$:

$\implies 2x+2=-2x+14$

$\implies 4x=12$

$\implies x=3$

Substitute found value of $x$ into Equation 2 and solve for $y$:

$\implies y=2(3)+2=8$

Therefore, the solution to the system is (3, 8).  

This is the point of intersection of the two lines.