Question

solve the system of two equations using substitution.

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

(2, 10)
(-2, 4)
(-2, -4)
(2, 8)

Answer 1

To solve the system of equations using substitution, we'll substitute the expression for \(y\) from the first equation into the second equation.

The equations are:
1. \(y = 2 + 3x\)
2. \(4x - 3y = -16\)

We will substitute \(y\) from the first equation into the second equation:

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

Now, distribute the -3:
\[
4x - 6 - 9x = -16
\]

Combine like terms:
\[
4x - 9x - 6 = -16
\]
\[
-5x - 6 = -16
\]

Now, add 6 to both sides:
\[
-5x = -10
\]

Now, divide by -5:
\[
x = 2
\]

Now, we need to find \(y\) using the expression for \(y\):
\[
y = 2 + 3x
\]
\[
y = 2 + 3(2)
\]
\[
y = 2 + 6
\]
\[
y = 8
\]

So, the solution to the system of equations is:
\[
(x, y) = (2, 8)
\]

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