Question

Solve the system of two equations using substitution. y=2+3x 4x−3y=−16 (1 point)

(2, 10)

(−2, 4)

(2, 8)

(−2, −4)

Answer 1

To solve the system of equations using substitution, we can start with the two given equations:

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

First, 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 the left side:

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

Combine like terms:

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

Now, add 6 to both sides:

\[
-5x = -10
\]

Next, divide both sides by -5:

\[
x = 2
\]

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

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

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

Therefore, the correct answer is:

**(2, 8)**