To solve the given system of equations:
[tex]\[
\begin{aligned}
x - 2y &= 5 \\
3x + 15y &= -6
\end{aligned}
\][/tex]
Step-by-Step Solution:
1. Express [tex]\(y\)[/tex] from the first equation:
[tex]\[
x - 2y = 5 \\
\Rightarrow x = 5 + 2y
\][/tex]
2. Substitute [tex]\(x = 5 + 2y\)[/tex] into the second equation:
[tex]\[
3(5 + 2y) + 15y = -6 \\
\Rightarrow 15 + 6y + 15y = -6 \\
\Rightarrow 21y = -21 \\
\Rightarrow y = -1
\][/tex]
3. Substitute [tex]\(y = -1\)[/tex] back into [tex]\(x = 5 + 2y\)[/tex]:
[tex]\[
x = 5 + 2(-1) \\
\Rightarrow x = 5 - 2 \\
\Rightarrow x = 3
\][/tex]
So, the solution to the system of equations is [tex]\((3, -1)\)[/tex].
Identifying the Correct Graph:
The graph that represents the given system of equations correctly should intersect at the point [tex]\((3, -1)\)[/tex]. Among the provided options, the correct graph is graph [tex]\(A\)[/tex].
Final Sentence Completion:
The graph that correctly represents the given system of equations is graph A, and the solution to the system is:(3, -1).
