Question

Solve the system of equations.
2x+6y=−18

x=5y−1
(1 point)
Responses

(−6, −1)

(5.25, 1.25)

(4, 1)

(−7.25, −1.25)

Answer 1

To solve the system of 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 \(x\):

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

Expanding this:

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

Combining like terms:

\[
16y - 2 = -18
\]

Adding 2 to both sides:

\[
16y = -16
\]

Dividing by 16:

\[
y = -1
\]

Now substitute \(y = -1\) back into the second equation to find \(x\):

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

Calculating this gives:

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

So the solution to the system of equations is:

\[
(x, y) = (-6, -1)
\]

Thus, the correct response is:

**(−6, −1)**