Question

y = -2x + 8
y = 4x - 10


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.

The solution of the system of
equation is (__).

Answer 1

To find the solution of the system of equations given by:

1. \( y = -2x + 8 \)
2. \( y = 4x - 10 \)

we can solve for \( x \) by setting the two right-hand sides equal to each other since both expressions equal \( y \):

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

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

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

\[
8 = 6x - 10
\]

2. Add \( 10 \) to both sides:

\[
18 = 6x
\]

3. Divide both sides by \( 6 \):

\[
x = 3
\]

Next, we can substitute \( x = 3 \) back into either equation to find \( y \). We'll use the first equation:

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

Calculating this gives:

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

Thus, the solution of the system of equations is:

\[
\text{The solution of the system of equations is } (3, 2).
\]