High School

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 given system of equations using the elimination method, follow these steps:

Given:
1. [tex]\(5a + 5b = 25\)[/tex]
2. [tex]\(-5a + 5b = 35\)[/tex]

Step 1: Add the two equations together to eliminate [tex]\(a\)[/tex]:

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

Step 2: Simplify the left side:

The terms [tex]\(5a\)[/tex] and [tex]\(-5a\)[/tex] cancel each other out, resulting in:

[tex]\[
5b + 5b = 10b
\][/tex]

Step 3: Simplify the right side:

[tex]\[
25 + 35 = 60
\][/tex]

So, the resulting equation is:

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

Therefore, the correct equation after using elimination is [tex]\(10b = 60\)[/tex].

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