Answer :
To solve the given system of equations using the elimination method, follow these steps:
You have the system:
[tex]\[
\begin{align*}
1. & \quad 5a + 5b = 25 \\
2. & \quad -5a + 5b = 35 \\
\end{align*}
\][/tex]
The goal of elimination is to remove one of the variables by adding or subtracting the equations.
1. Add the two equations together to eliminate the variable [tex]\(a\)[/tex]:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
2. Simplify the resulting equation:
- The terms involving [tex]\(a\)[/tex] will cancel each other out:
[tex]\[
5a - 5a = 0
\][/tex]
- Add the terms involving [tex]\(b\)[/tex]:
[tex]\[
5b + 5b = 10b
\][/tex]
- So, you have:
[tex]\[
10b = 60
\][/tex]
The resulting equation after using elimination is:
[tex]\[
10b = 60
\][/tex]
This equation can then be solved for [tex]\(b\)[/tex] if needed. This step-by-step process shows how elimination was used to derive the equation [tex]\(10b = 60\)[/tex].
You have the system:
[tex]\[
\begin{align*}
1. & \quad 5a + 5b = 25 \\
2. & \quad -5a + 5b = 35 \\
\end{align*}
\][/tex]
The goal of elimination is to remove one of the variables by adding or subtracting the equations.
1. Add the two equations together to eliminate the variable [tex]\(a\)[/tex]:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
2. Simplify the resulting equation:
- The terms involving [tex]\(a\)[/tex] will cancel each other out:
[tex]\[
5a - 5a = 0
\][/tex]
- Add the terms involving [tex]\(b\)[/tex]:
[tex]\[
5b + 5b = 10b
\][/tex]
- So, you have:
[tex]\[
10b = 60
\][/tex]
The resulting equation after using elimination is:
[tex]\[
10b = 60
\][/tex]
This equation can then be solved for [tex]\(b\)[/tex] if needed. This step-by-step process shows how elimination was used to derive the equation [tex]\(10b = 60\)[/tex].
