Question

Solving Equations Using Substitution Quick Check
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Question
Solve the system of two equations using substitution.
y=2+3x

4x−3y=−16
(1 point)
Responses

(−2, −4)
left parenthesis negative 2 comma negative 4 right parenthesis

(2, 10)
left parenthesis 2 comma 10 right parenthesis

(−2, 4)
left parenthesis negative 2 comma 4 right parenthesis

(2, 8)

Answer 1

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

1. \(y = 2 + 3x\)
2. \(4x - 3y = -16\)

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

Substituting \(y = 2 + 3x\) into the second equation gives us:

\[
4x - 3(2 + 3x) = -16
\]

Now, simplify the equation:

\[
4x - 6 - 9x = -16
\]

Combine like terms:

\[
-5x - 6 = -16
\]

Next, add 6 to both sides:

\[
-5x = -10
\]

Now, divide both sides by -5:

\[
x = 2
\]

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

\[
y = 2 + 3(2) = 2 + 6 = 8
\]

Thus, the solution to the system of equations is \((x, y) = (2, 8)\).

So the correct response is:

\((2, 8)\)