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 4 right parenthesis

(−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
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Answer 1

To solve the system of equations using substitution, let's start with the equations given:

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

Next, we'll use the first equation to substitute for \( y \) in the second equation.

Substituting \( y \) in the second equation:

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

Now, simplify the equation:

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

Combine like terms:

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

Now, add 6 to both sides:

\[ -5x = -10 \]

Now, divide by -5:

\[ x = 2 \]

Now that we have \( x \), we can substitute it back into the first equation to find \( y \):

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

So we have:

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

Thus, the solution to the system of equations is:

\((2, 8)\)

The correct response is: \((2, 8)\)