Answer :
Certainly! Let's solve the given system of equations using the elimination method step-by-step.
The system of equations is:
[tex]\[
\left\{
\begin{array}{r}
5a + 5b = 25 \\
-5a + 5b = 35
\end{array}
\right.
\][/tex]
To use the elimination method, we need to add or subtract the equations in a way that eliminates one of the variables. In this case, let's add the two equations together to eliminate [tex]\(a\)[/tex]:
1. Write down the equations:
[tex]\[
5a + 5b = 25
\][/tex]
[tex]\[
-5a + 5b = 35
\][/tex]
2. Add the two equations together:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
3. Combine like terms:
[tex]\[
5a - 5a + 5b + 5b = 60
\][/tex]
[tex]\[
0a + 10b = 60
\][/tex]
[tex]\[
10b = 60
\][/tex]
The resulting equation when elimination is used is:
[tex]\[
10b = 60
\][/tex]
So, the correct answer is:
[tex]\[ \boxed{10b = 60} \][/tex]
The system of equations is:
[tex]\[
\left\{
\begin{array}{r}
5a + 5b = 25 \\
-5a + 5b = 35
\end{array}
\right.
\][/tex]
To use the elimination method, we need to add or subtract the equations in a way that eliminates one of the variables. In this case, let's add the two equations together to eliminate [tex]\(a\)[/tex]:
1. Write down the equations:
[tex]\[
5a + 5b = 25
\][/tex]
[tex]\[
-5a + 5b = 35
\][/tex]
2. Add the two equations together:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
3. Combine like terms:
[tex]\[
5a - 5a + 5b + 5b = 60
\][/tex]
[tex]\[
0a + 10b = 60
\][/tex]
[tex]\[
10b = 60
\][/tex]
The resulting equation when elimination is used is:
[tex]\[
10b = 60
\][/tex]
So, the correct answer is:
[tex]\[ \boxed{10b = 60} \][/tex]
