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

[tex]
\[
\left\{
\begin{array}{r}
5a + 5b = 25 \\
-5a + 5b = 35
\end{array}
\right.
\]
[/tex]

A. [tex]10a = 60[/tex]
B. [tex]10b = 60[/tex]
C. [tex]-10a = 60[/tex]
D. [tex]-10b = 60[/tex]

Answer :

Sure, let's solve this system of equations step by step using the elimination method.

We start with the system of equations:
[tex]\[
\begin{cases}
5a + 5b = 25 \\
-5a + 5b = 35
\end{cases}
\][/tex]

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

2. Eliminate one variable: To eliminate [tex]\(a\)[/tex], we add Equation 1 and Equation 2:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]

3. Perform the addition:
[tex]\[
(5a - 5a) + (5b + 5b) = 25 + 35
\][/tex]
Simplifying the left-hand side, we get:
[tex]\[
0 + 10b = 60
\][/tex]
Therefore:
[tex]\[
10b = 60
\][/tex]

So, the resulting equation when using elimination to solve the given system is:
[tex]\[
10b = 60
\][/tex]

Thus, the correct answer is:
[tex]\[
10b = 60
\][/tex]

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