High School

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 :

To solve the given system of equations using the elimination method, follow the steps below:

The given system of equations is:
[tex]\[
\begin{cases}
5a + 5b = 25 \quad \text{(Equation 1)} \\
-5a + 5b = 35 \quad \text{(Equation 2)}
\end{cases}
\][/tex]

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

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

2. Combine like terms:

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

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

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

The resulting equation when using elimination on the given system is:
[tex]\[
\boxed{10b = 60}
\][/tex]

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