Question

Solving Equations Using Substitution Quick Check 1 of 51 of 5 Items 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, −4) left parenthesis negative 2 comma negative 4 right parenthesis (2, 10) left parenthesis 2 comma 10 right parenthesis (2, 8)

Answer 1

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

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

We can substitute Equation 1 into Equation 2.

Substituting \( y \) in Equation 2:

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

Now, let's simplify this equation step by step:

1. Distribute \( -3 \):
\[
4x - 6 - 9x = -16
\]

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

3. Add 6 to both sides:
\[
-5x = -10
\]

4. Divide by -5:
\[
x = 2
\]

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

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

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

The correct response is:

**(2, 8)**