Question

How do we use substitution in the following system of equations to solve for x?

y = 2 + 3x
4x - 3y = -16



(1 point)
Responses

Replace x with 4x-3y. Rewrite the first equation: 4x-3y=-16x
Replace x with 4x-3y. Rewrite the first equation: 4x-3y=-16x

Multiply everything by 2.
Multiply everything by 2.

Replace y with (2+3x) Rewrite the second equation: 4x-3(2+3x) -16.

Answer 1

To solve the given system of equations using substitution, we can follow these steps:

1. **Identify the equations**:
- \( y = 2 + 3x \) (Equation 1)
- \( 4x - 3y = -16 \) (Equation 2)

2. **Substitute \(y\) from Equation 1 into Equation 2**:
- Since we have \(y\) expressed in terms of \(x\) from Equation 1, we can substitute this expression into Equation 2.

3. **Replacing \(y\)**:
- Substitute \(y = 2 + 3x\) into Equation 2:
\[
4x - 3(2 + 3x) = -16
\]

4. **Simplify the equation**:
- Distribute \(-3\):
\[
4x - 6 - 9x = -16
\]
- Combine like terms:
\[
-5x - 6 = -16
\]

5. **Solve for \(x\)**:
- Add \(6\) to both sides:
\[
-5x = -10
\]
- Divide by \(-5\):
\[
x = 2
\]

Thus, the substitution is done correctly. Therefore, the correct option response is:

**Replace y with (2 + 3x). Rewrite the second equation: 4x - 3(2 + 3x) = -16.**