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:

We have the system of equations:
1. [tex]\( 5a + 5b = 25 \)[/tex]
2. [tex]\( -5a + 5b = 35 \)[/tex]

The goal of the elimination method is to eliminate one of the variables by adding or subtracting the equations. Here, we can add these two equations to eliminate the variable [tex]\( a \)[/tex].

Step 1: Add the two equations together.

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

By adding, the terms with [tex]\( a \)[/tex] cancel each other out because [tex]\( 5a + (-5a) = 0 \)[/tex].

This simplifies to:
[tex]\[
0a + 10b = 60
\][/tex]

Step 2: Simplify the equation.

Since [tex]\( 0a \)[/tex] doesn't contribute anything, the equation is simplified to:
[tex]\[
10b = 60
\][/tex]

Therefore, the resulting equation after using elimination is:
[tex]\[
10b = 60
\][/tex]