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 4 right parenthesis

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

(2, 8)
left parenthesis 2 comma 8 right parenthesis

(2, 10)
left parenthesis 2 comma 10 right parenthesis
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Answer 1

To solve the system of equations using substitution, let's start with the equations given:

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

Next, we'll use the first equation to substitute for \( y \) in the second equation.

Substituting \( y \) in the second equation:

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

Now, simplify the equation:

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

Combine like terms:

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

Now, add 6 to both sides:

\[
-5x = -10
\]

Now, divide by -5:

\[
x = 2
\]

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

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

So we have:

\[
(x, y) = (2, 8)
\]

Thus, the solution to the system of equations is:

\((2, 8)\)

The correct response is:
\((2, 8)\)