Question

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

x=5y−1
(1 point)
Responses

(5.25, 1.25)
left parenthesis 5.25 comma 1.25 right parenthesis

(−6, −1)
left parenthesis negative 6 comma negative 1 right parenthesis

(4, 1)
left parenthesis 4 comma 1 right parenthesis

(−7.25, −1.25)

Answer 1

To solve the system of equations:

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

We can substitute the second equation into the first equation.

Substituting \(x\) in the first equation:

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

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 we can find \(x\) using the second equation \(x = 5y - 1\):

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

Thus, the solution to the system of equations is:

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

So the correct response is \((-6, -1)\).