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 :

Sure, let's solve this problem step by step without referring to the Python code provided.

We are given the following system of equations:
[tex]\[
\left\{\begin{array}{r}
5a + 5b = 25 \\
-5a + 5b = 35
\end{array}\right.
\][/tex]

To use the elimination method, we'll add the two equations to eliminate the variable [tex]\(a\)[/tex]:

1. Write the equations clearly:
[tex]\[
5a + 5b = 25 \quad \text{(Equation 1)}
\][/tex]
[tex]\[
-5a + 5b = 35 \quad \text{(Equation 2)}
\][/tex]

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

3. Combine the like terms:
[tex]\[
(5a - 5a) + (5b + 5b) = 25 + 35
\][/tex]
[tex]\[
0a + 10b = 60
\][/tex]
[tex]\[
10b = 60
\][/tex]

So, the resulting equation when using elimination to solve the given system is:
[tex]\[
10b = 60
\][/tex]

Therefore, the correct answer is [tex]\(10b = 60\)[/tex].