Answer :
To solve the given system of equations using elimination, we 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. The method of elimination involves adding or subtracting the equations to eliminate one of the variables. Here, we notice that adding Equation 1 and Equation 2 will eliminate the variable [tex]\(a\)[/tex] because the coefficients of [tex]\(a\)[/tex] are [tex]\(5\)[/tex] and [tex]\(-5\)[/tex], which are opposites.
3. Add the two equations together:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
4. The terms involving [tex]\(a\)[/tex] cancel each other out:
[tex]\[
0a + 10b = 60
\][/tex]
5. This simplifies to:
[tex]\[
10b = 60
\][/tex]
Therefore, the resulting equation when elimination is used to solve the given system is [tex]\(10b = 60\)[/tex].
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. The method of elimination involves adding or subtracting the equations to eliminate one of the variables. Here, we notice that adding Equation 1 and Equation 2 will eliminate the variable [tex]\(a\)[/tex] because the coefficients of [tex]\(a\)[/tex] are [tex]\(5\)[/tex] and [tex]\(-5\)[/tex], which are opposites.
3. Add the two equations together:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
4. The terms involving [tex]\(a\)[/tex] cancel each other out:
[tex]\[
0a + 10b = 60
\][/tex]
5. This simplifies to:
[tex]\[
10b = 60
\][/tex]
Therefore, the resulting equation when elimination is used to solve the given system is [tex]\(10b = 60\)[/tex].
