Question

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, 10)
left parenthesis 2 comma 10 right parenthesis

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

(2, 8)

Answer 1

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

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

We can substitute Equation 1 into Equation 2.

Substituting \( y \) in Equation 2:

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

Now, distribute \(-3\):

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

Combine like terms:

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

Now, isolate \(x\):

\[
-5x = -16 + 6
\]
\[
-5x = -10
\]
\[
x = 2
\]

Now that we have \(x\), we can substitute it back into Equation 1 to find \(y\):

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

The solution to the system of equations is:

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

Thus, the answer is:

(2, 8)