Select the correct answer from each drop-down menu.

Use the system of equations and graphs below to complete the sentence.

[tex]
\begin{aligned}
x - 2y & = 5 \\
3x + 15y & = -6
\end{aligned}
[/tex]

Graph A

Graph B

Graph C

Graph D

The graph that correctly represents the given system of equations is graph [tex]$\square$[/tex], and the solution to the system is ([tex]$\square$[/tex], [tex]$\square$[/tex]).



Answer :

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).