Question

The first equation tells you that y equals 2x−8. So, one way to start solving this system of equations is to substitute 2x−8 anywhere you see y in the second equation. Go for it. Substitute 2x−8 for y in the second equation.
y= 2x−8
x= −3y+18
x = −3(
) + 1

Answer 1

Sure! Given the first equation \( y = 2x - 8 \), we can substitute \( y \) into the second equation \( x = -3y + 18 \).

So substituting \( 2x - 8 \) for \( y \) gives us:

\[
x = -3(2x - 8) + 18
\]

Now, let's simplify this equation step-by-step:

1. Distribute the -3:
\[
x = -6x + 24 + 18
\]

2. Combine like terms:
\[
x = -6x + 42
\]

3. Add \( 6x \) to both sides:
\[
x + 6x = 42 \\
7x = 42
\]

4. Finally, divide by 7:
\[
x = 6
\]

Now that we have \( x \), we can substitute it back into the first equation to find \( y \):

\[
y = 2(6) - 8 \\
y = 12 - 8 \\
y = 4
\]

Thus, the solution to the system of equations is \( x = 6 \) and \( y = 4 \).