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

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)

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.