Question

Solving Equations Using Substitution Quick Check
2 of 52 of 5 Items


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)
left parenthesis negative 7.25 comma negative 1.25 right parenthesis

Answer 1

To solve the system of equations given by:

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

we can use substitution.

First, substitute \( x \) in the first equation:

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

Now, simplify the equation:

- Distributing \( 2 \):

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

Combine like terms:

\[
16y - 2 = -18
\]

Next, add \( 2 \) to both sides:

\[
16y = -16
\]

Now, divide by \( 16 \):

\[
y = -1
\]

Now that we have \( y \), substitute it back into the equation for \( x \):

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

Calculating that:

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

So the solution to the system of equations is:

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

Based on the provided choices, the correct answer is:

\((−6, −1)\)