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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]

To solve the given system of equations using the elimination method, we want to eliminate one of the variables by either adding or subtracting the equations. Let's take a look at the system:

1. [tex]$5a + 5b = 25$[/tex]
2. [tex]$-5a + 5b = 35$[/tex]

To use elimination, we'll add these two equations together:

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

This simplifies to:

[tex]\[
5a - 5a + 5b + 5b = 60
\][/tex]

Notice that the [tex]$5a$[/tex] and [tex]$-5a$[/tex] terms cancel each other out:

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

So, we get the resulting equation:

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

Therefore, the correct answer is [tex]$10b = 60$[/tex].