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, 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 two equations:

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

We can 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, simplify: \[ 4x - 6 - 9x = -16 \]

Combine like terms: \[ -5x - 6 = -16 \]

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, the solution to the system of equations is: \[ (x, y) = (2, 8) \]

The correct answer is \( \boxed{(2, 8)} \).