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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, let's go through the steps:

The given system of equations is:

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

Our goal is to eliminate one of the variables. In this case, let's eliminate the variable [tex]$a$[/tex].

To do this, we need to add the two equations together:

- Adding the left sides: [tex]$(5a + 5b) + (-5a + 5b)$[/tex]
- Adding the right sides: [tex]$25 + 35$[/tex]

When we add the left sides:

- [tex]$5a + (-5a) = 0a$[/tex], so they cancel each other out.
- [tex]$5b + 5b = 10b$[/tex]

Thus, the resulting equation after adding the two left sides is:

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

Since [tex]$0a$[/tex] is just zero, we get:

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

This is the resultant equation when using elimination on the given system.

Therefore, the correct result from using the elimination method is:

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