Solving Equations Using Substitution Quick Check

Question

2 of 52 of 5 Items

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

x=5y−1
(1 point)
Responses

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

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

(−7.25, −1.25)
left parenthesis negative 7.25 comma negative 1.25 right parenthesis

(−6, −1)

Answer 1

To solve the system of equations using substitution, we have the following equations:

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

We can substitute Equation 2 (the expression for \(x\)) into Equation 1.

Substituting \(x = 5y - 1\) into Equation 1:

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

Now, distribute the 2:

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

Combining like terms:

\[ 16y - 2 = -18 \]

Now, add 2 to both sides:

\[ 16y = -16 \]

Divide by 16:

\[ y = -1 \]

Now that we have \(y\), we can substitute it back into Equation 2 to find \(x\):

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

Thus, the solution to the system of equations is \((-6, -1)\).

Comparing this with the given options, the correct response is:

(−6, −1)