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)
left parenthesis 2 comma 8 right parenthesis

Answer 1

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

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

We can substitute Equation 1 into Equation 2. First, we will replace \( y \) in Equation 2 with the expression we have from Equation 1:

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

Now, distribute \(-3\) to both terms inside the parentheses:

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

Combine like terms:

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

Next, we add \( 6 \) to both sides:

\[ -5x = -10 \]

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

\[ x = 2 \]

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

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

\[ y = 2 + 6 \]

\[ y = 8 \]

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

The correct response is:

(2, 8)