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

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

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

Answer :

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

Step 1. Add the two equations together to eliminate [tex]$a$[/tex]. Adding the left-hand sides and right-hand sides, we have:
[tex]$$
(5a + (-5a)) + (5b + 5b) = 25 + 35.
$$[/tex]

Step 2. Simplify the expression. Notice that [tex]$5a + (-5a) = 0$[/tex], and [tex]$5b + 5b = 10b$[/tex]. Also, [tex]$25 + 35 = 60$[/tex]. So, the equation becomes:
[tex]$$
10b = 60.
$$[/tex]

This equation, [tex]$10b = 60$[/tex], is the resulting equation when elimination is used to solve the given system.

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