Solve the system of two equations using substitution.

Question

y=2+3x
4x−3y=−16 (1 point)
Responses

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

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

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

(2, 10)

Answer 1

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

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

We'll 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, let's simplify the equation:

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

Combine like terms:

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

Add \(6\) to both sides:

\[ -5x = -10 \]

Now, divide both sides by \(-5\):

\[ x = 2 \]

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

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

Calculating \(y\):

\[ y = 2 + 6 = 8 \]

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

The correct response is:

\((2, 8)\)