To solve the system of equations:
[tex]\[
\begin{array}{c}
x - 2y = 15 \\
2x + 4y = -18
\end{array}
\][/tex]
First, let's use the substitution or elimination method to find the solution:
1. Start with the first equation:
[tex]\[
x - 2y = 15 \quad \text{(Equation 1)}
\][/tex]
2. Solve Equation 1 for [tex]\( x \)[/tex]:
[tex]\[
x = 15 + 2y
\][/tex]
3. Substitute [tex]\( x \)[/tex] into the second equation:
[tex]\[
2(15 + 2y) + 4y = -18 \quad \text{(Equation 2)}
\][/tex]
4. Expand and simplify:
[tex]\[
30 + 4y + 4y = -18
\][/tex]
[tex]\[
30 + 8y = -18
\][/tex]
5. Isolate [tex]\( y \)[/tex]:
[tex]\[
8y = -18 - 30
\][/tex]
[tex]\[
8y = -48
\][/tex]
[tex]\[
y = -6
\][/tex]
6. Now substitute [tex]\( y = -6 \)[/tex] back into the first equation to find [tex]\( x \)[/tex]:
[tex]\[
x - 2(-6) = 15
\][/tex]
[tex]\[
x + 12 = 15
\][/tex]
[tex]\[
x = 3
\][/tex]
Hence, the solution to the system of equations is:
[tex]\[
x = 3, \, y = -6
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{C: x=3, y=-6}
\][/tex]
