Answer :
To solve the given system of equations using the elimination method, follow these steps:
1. Identify the System of Equations:
[tex]\[
\begin{aligned}
&1) \quad 5a + 5b = 25 \\
&2) \quad -5a + 5b = 35 \\
\end{aligned}
\][/tex]
2. Add the Equations:
By adding the two equations, you aim to eliminate one of the variables. Here, you want to eliminate the variable [tex]\(a\)[/tex].
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
When you add these equations together, the [tex]\(a\)[/tex] terms cancel each other out:
[tex]\[
5a + (-5a) = 0
\][/tex]
3. Simplify the Resulting Equation:
The result of adding the two equations is:
[tex]\[
0a + 10b = 60
\][/tex]
Which simplifies to:
[tex]\[
10b = 60
\][/tex]
This equation, [tex]\(10b = 60\)[/tex], is the resulting equation after applying the elimination method to the given system of equations.
1. Identify the System of Equations:
[tex]\[
\begin{aligned}
&1) \quad 5a + 5b = 25 \\
&2) \quad -5a + 5b = 35 \\
\end{aligned}
\][/tex]
2. Add the Equations:
By adding the two equations, you aim to eliminate one of the variables. Here, you want to eliminate the variable [tex]\(a\)[/tex].
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
When you add these equations together, the [tex]\(a\)[/tex] terms cancel each other out:
[tex]\[
5a + (-5a) = 0
\][/tex]
3. Simplify the Resulting Equation:
The result of adding the two equations is:
[tex]\[
0a + 10b = 60
\][/tex]
Which simplifies to:
[tex]\[
10b = 60
\][/tex]
This equation, [tex]\(10b = 60\)[/tex], is the resulting equation after applying the elimination method to the given system of equations.
