Question

Solve the system of two equations using substitution.
y=2+3x

4x−3y=−16
(1 point)
Responses

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

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

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

(−2, −4)

Answer 1

To solve the system of equations using substitution, we start with the two equations:

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

First, we substitute the expression for \( y \) from the first equation into the second equation:

Substituting \( y \) in the second equation:

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

Now, distribute the \(-3\):

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

Combine like terms:

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

Next, add 6 to both sides:

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

Now, divide by \(-5\):

\[
x = 2
\]

Now that we have \( x \), we can find \( y \) using the first equation:

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

So, the solution to the system of equations is \( (2, 8) \).

Thus, the answer is:

\((2, 8)\)