To solve the system of equations:
[tex]\[
\begin{aligned}
y - 15 &= 3x \\
-2x + 5y &= -3
\end{aligned}
\][/tex]
we can use the substitution method.
1. First, solve the first equation for [tex]\( y \)[/tex]:
[tex]\[
y - 15 = 3x
\][/tex]
Add 15 to both sides:
[tex]\[
y = 3x + 15
\][/tex]
2. Substitute [tex]\( y = 3x + 15 \)[/tex] into the second equation:
[tex]\[
-2x + 5(3x + 15) = -3
\][/tex]
3. Simplify and solve for [tex]\( x \)[/tex]:
[tex]\[
-2x + 15x + 75 = -3
\][/tex]
Combine like terms:
[tex]\[
13x + 75 = -3
\][/tex]
Subtract 75 from both sides:
[tex]\[
13x = -3 - 75
\][/tex]
[tex]\[
13x = -78
\][/tex]
Divide by 13:
[tex]\[
x = -6
\][/tex]
4. Substitute [tex]\( x = -6 \)[/tex] back into the expression for [tex]\( y \)[/tex]:
[tex]\[
y = 3(-6) + 15
\][/tex]
Simplify:
[tex]\[
y = -18 + 15
\][/tex]
[tex]\[
y = -3
\][/tex]
Therefore, the solution to the system of equations is [tex]\( x = -6 \)[/tex] and [tex]\( y = -3 \)[/tex]. The correct answer is:
[tex]\[
\boxed{(-6, -3)}
\][/tex]
So, the correct choice is:
A. [tex]\((-6, -3)\)[/tex]
