Let's solve the problem step by step.
We are given two equations:
1. [tex]\( 5x + 10y = 18 \)[/tex]
2. [tex]\( x = y - 6 \)[/tex]
We need to substitute [tex]\( y - 6 \)[/tex] for [tex]\( x \)[/tex] in the first equation. Here's the detailed process:
1. Start with the first equation:
[tex]\[
5x + 10y = 18
\][/tex]
2. Substitute [tex]\( x \)[/tex] with [tex]\( y - 6 \)[/tex]:
[tex]\[
5(y - 6) + 10y = 18
\][/tex]
3. Distribute the 5 inside the parentheses:
[tex]\[
5y - 30 + 10y = 18
\][/tex]
So, the resulting equation after substitution is:
[tex]\[
5y - 30 + 10y = 18
\][/tex]
Among the provided options, the correct one is:
[tex]\[
5y - 30 + 10y = 18
\][/tex]
So the correct equation is indeed:
[tex]\[
5y - 30 + 10y = 18
\][/tex]
