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, 10)
left parenthesis 2 comma 10 right parenthesis

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

Answer 1

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

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

We will substitute Equation 1 into Equation 2.

Step 1: Substitute \( y \) from Equation 1 into Equation 2.

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

Step 2: Distribute the \(-3\):

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

Step 3: Combine like terms:

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

Step 4: Add 6 to both sides:

\[ -5x = -10 \]

Step 5: Divide by -5:

\[ x = 2 \]

Step 6: Substitute \( x = 2 \) back into Equation 1 to find \( y \):

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

So the solution to the system of equations is:

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

The answer is:

\((2, 8)\) (which corresponds to the second option).