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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 system of equations using elimination, follow these steps:

1. Write down the given system of equations:

[tex]\[
\begin{cases}
5a + 5b = 25 \quad \text{(Equation 1)} \\
-5a + 5b = 35 \quad \text{(Equation 2)}
\end{cases}
\][/tex]

2. Add the two equations together:

When you add the equations, the terms involving [tex]\(a\)[/tex] will cancel out:

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

3. Simplify the resulting equation:

- The [tex]\(5a\)[/tex] and [tex]\(-5a\)[/tex] terms cancel each other out:
[tex]\[
0a + (5b + 5b) = 60
\][/tex]

- Simplify the terms:
[tex]\[
10b = 60
\][/tex]

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

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