Question

How do we use substitution in the following system of equations to solve for x?
y = 2 + 3x
4x - 3y = -16
A. Replace x with 4x-3y. Rewrite the first equation: 4x-3y=-16x
B. Multiply everything by 2.
C. • Replace y with (2+3x) Rewrite the second equation: 4x-3(2+3x) -16.

Answer 1

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

1. We are given the two equations:
\[
y = 2 + 3x \quad (1)
\]
\[
4x - 3y = -16 \quad (2)
\]

2. From equation (1), we can substitute \(y\) in equation (2):
\[
4x - 3(2 + 3x) = -16
\]

3. Now, distribute \(-3\) in the second equation:
\[
4x - 6 - 9x = -16
\]

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

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

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

Now that we have the value of \(x\), we can substitute back into equation (1) to find \(y\):
\[
y = 2 + 3(2) = 2 + 6 = 8
\]

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