Certainly! Let's solve the system of equations using substitution.
We are given two equations:
[tex]\[
\begin{array}{l}
1. \quad y = 2 + 3x \\
2. \quad 4x - 3y = -16
\end{array}
\][/tex]
Step 1: Substitute the expression for [tex]\( y \)[/tex] from the first equation into the second equation. The first equation is already solved for [tex]\( y \)[/tex], so we have:
[tex]\[
y = 2 + 3x
\][/tex]
Step 2: Substitute [tex]\( y = 2 + 3x \)[/tex] into the second equation:
[tex]\[
4x - 3(2 + 3x) = -16
\][/tex]
Step 3: Distribute the [tex]\(-3\)[/tex] inside the parentheses:
[tex]\[
4x - 6 - 9x = -16
\][/tex]
Step 4: Combine like terms on the left side:
[tex]\[
4x - 9x - 6 = -16 \\
-5x - 6 = -16
\][/tex]
Step 5: Add 6 to both sides of the equation to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
-5x = -16 + 6 \\
-5x = -10
\][/tex]
Step 6: Divide both sides by -5 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-10}{-5} \\
x = 2
\][/tex]
Step 7: Substitute [tex]\( x = 2 \)[/tex] back into the first equation ( [tex]\( y = 2 + 3x \)[/tex] ) to solve for [tex]\( y \)[/tex]:
[tex]\[
y = 2 + 3(2) \\
y = 2 + 6 \\
y = 8
\][/tex]
Therefore, the solution to the system of equations is [tex]\((x, y) = (2, 8)\)[/tex].
So, the correct answer is:
[tex]\[
(2, 8)
\][/tex]
