Answer :
To solve the given system of equations by elimination, we will follow these steps:
1. Write Down the Given System of 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:
By adding Equation 1 and Equation 2, you can eliminate the variable [tex]\(a\)[/tex] because their coefficients are opposites:
[tex]\[
\begin{align*}
(5a + 5b) + (-5a + 5b) &= 25 + 35 \\
5a + 5b - 5a + 5b &= 60 \\
10b &= 60
\end{align*}
\][/tex]
3. Resulting Equation:
The resulting equation is:
[tex]\[
10b = 60
\][/tex]
Therefore, after using the elimination method, we obtain the equation [tex]\(10b = 60\)[/tex]. This equation indicates the relationship of the variable [tex]\(b\)[/tex] in the given system of equations when [tex]\(a\)[/tex] is eliminated.
1. Write Down the Given System of 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:
By adding Equation 1 and Equation 2, you can eliminate the variable [tex]\(a\)[/tex] because their coefficients are opposites:
[tex]\[
\begin{align*}
(5a + 5b) + (-5a + 5b) &= 25 + 35 \\
5a + 5b - 5a + 5b &= 60 \\
10b &= 60
\end{align*}
\][/tex]
3. Resulting Equation:
The resulting equation is:
[tex]\[
10b = 60
\][/tex]
Therefore, after using the elimination method, we obtain the equation [tex]\(10b = 60\)[/tex]. This equation indicates the relationship of the variable [tex]\(b\)[/tex] in the given system of equations when [tex]\(a\)[/tex] is eliminated.
