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Which could be the resulting equation when elimination is used to solve the given system of equations?

[tex]
\[
\begin{cases}
5a + 5b = 25 \\
-5a + 5b = 35
\end{cases}
\]
[/tex]

A. [tex]10a = 60[/tex]

B. [tex]10b = 60[/tex]

C. [tex]-10a = 60[/tex]

D. [tex]-10b = 60[/tex]

Answer :

To solve the given system of equations using elimination, we follow these steps:

We have the system:
1. [tex]\(5a + 5b = 25\)[/tex]
2. [tex]\(-5a + 5b = 35\)[/tex]

The elimination method involves adding the two equations to eliminate one of the variables. Let's add these equations together:

[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]

Simplifying this, we see that the [tex]\(5a\)[/tex] and [tex]\(-5a\)[/tex] terms cancel each other out:

[tex]\[
0a + 10b = 60
\][/tex]

This simplifies to:

[tex]\[
10b = 60
\][/tex]

So, the resulting equation when elimination is used is [tex]\(10b = 60\)[/tex].

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