Question

Solve the system of equations.
2x + 6y = -18
x = 5y - 1

Answer 1

To solve the system of equations, we have the following two equations:

1. \( 2x + 6y = -18 \)
2. \( x = 5y - 1 \)

We can substitute the expression for \( x \) from the second equation into the first equation.

Substituting \( x \) in the first equation:

\[
2(5y - 1) + 6y = -18
\]

Now, distribute:

\[
10y - 2 + 6y = -18
\]

Combine like terms:

\[
16y - 2 = -18
\]

Add 2 to both sides:

\[
16y = -16
\]

Dividing both sides by 16:

\[
y = -1
\]

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

\[
x = 5(-1) - 1
\]

Calculating that gives:

\[
x = -5 - 1 = -6
\]

So the solution to the system of equations is:

\[
x = -6, \quad y = -1
\]

In ordered pair form, the solution is:

\[
\boxed{(-6, -1)}
\]