Question

Question

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.

(2 points)

(
)
Skip to navigation

Answer 1

To find the solution of the system of the two linear equations \( y = 4x - 10 \) and \( y = -2x + 8 \), we can set the two equations equal to each other since both are equal to \( y \):

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

Now, we will solve for \( x \):

1. Add \( 2x \) to both sides:

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

This simplifies to:

\[
6x - 10 = 8
\]

2. Next, add \( 10 \) to both sides:

\[
6x = 18
\]

3. Now, divide both sides by \( 6 \):

\[
x = 3
\]

With \( x = 3 \), we can now substitute this back into either of the original equations to find \( y \). Let's use the second equation:

\[
y = -2(3) + 8
\]

Calculating gives:

\[
y = -6 + 8 = 2
\]

So the solution of the system is:

\[
(x, y) = (3, 2)
\]

In summary, the solution to the system of equations is:

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