College

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:

1. Identify the System of Equations:

[tex]\[
\begin{aligned}
&1) \quad 5a + 5b = 25 \\
&2) \quad -5a + 5b = 35 \\
\end{aligned}
\][/tex]

2. Add the Equations:

By adding the two equations, you aim to eliminate one of the variables. Here, you want to eliminate the variable [tex]\(a\)[/tex].

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

When you add these equations together, the [tex]\(a\)[/tex] terms cancel each other out:

[tex]\[
5a + (-5a) = 0
\][/tex]

3. Simplify the Resulting Equation:

The result of adding the two equations is:

[tex]\[
0a + 10b = 60
\][/tex]

Which simplifies to:

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

This equation, [tex]\(10b = 60\)[/tex], is the resulting equation after applying the elimination method to the given system of equations.