Question

Use the image to answer the question.



Review the graphs of a system of these two linear equations in two variables: y=4x−10 and y=−2x+8 Find the solution of the system.

(1 point)
The solution of the system of equations is ().

Answer 1

To find the solution of the system of equations given by \( y = 4x - 10 \) and \( y = -2x + 8 \), we need to set the equations equal to each other:

\[
4x - 10 = -2x + 8
\]

Now, let's solve for \( x \):

1. Add \( 2x \) to both sides:
\[
4x + 2x - 10 = 8
\]
\[
6x - 10 = 8
\]

2. Add \( 10 \) to both sides:
\[
6x = 18
\]

3. Divide by \( 6 \):
\[
x = 3
\]

Now, substitute \( x = 3 \) back into one of the original equations to find \( y \). We'll use \( y = 4x - 10 \):

\[
y = 4(3) - 10
\]
\[
y = 12 - 10
\]
\[
y = 2
\]

Thus, the solution to the system of equations is:

\[
\boxed{(3, 2)}
\]