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].
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].
