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, 10) left parenthesis 2 comma 10 right parenthesis (2, 8) left parenthesis 2 comma 8 right parenthesis (−2, −4)

Answer 1

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

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

We can substitute the expression for \( y \) from the first equation into the second equation.

**Step 1: Substitute for \( y \)**

Substituting \( y \) in the second equation:

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

**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 \( x \) back into the first equation to find \( y \)**

Now we substitute \( x = 2 \) back into the first equation:

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

\[
y = 2 + 6 = 8
\]

**Step 7: Write the solution as an ordered pair**

The solution to the system of equations is:

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

So the answer is \( (2, 8) \).