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]10a = 60[/tex]
C. [tex]10b = 60[/tex]
D. [tex]-10b = 60[/tex]

Answer :

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

1. Write down the given equations:

[tex]\[
\begin{align*}
5a + 5b &= 25 \quad \text{(Equation 1)} \\
-5a + 5b &= 35 \quad \text{(Equation 2)}
\end{align*}
\][/tex]

2. Add the two equations together:

When you add Equation 1 and Equation 2, the terms involving [tex]\(a\)[/tex] will cancel out (because [tex]\(5a\)[/tex] and [tex]\(-5a\)[/tex] sum to 0). Here's how the addition looks step-by-step:

[tex]\[
\begin{align*}
(5a + 5b) + (-5a + 5b) &= 25 + 35
\end{align*}
\][/tex]

Simplifying the left side, the [tex]\(a\)[/tex] terms cancel each other:

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

On the right side, the constants add up to:

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

3. Resulting equation after elimination:

After performing the addition, we are left with the equation:

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

This resulting equation, [tex]\(10b = 60\)[/tex], is what you get after using the elimination method to solve the given system of equations by removing the variable [tex]\(a\)[/tex].