Answer :
To solve the given system of equations using elimination, we follow these steps:
1. Write down the given system of equations:
[tex]\[
\begin{align*}
(1) & \quad 5a + 5b = 25 \\
(2) & \quad -5a + 5b = 35
\end{align*}
\][/tex]
2. Eliminate one of the variables:
To eliminate [tex]\( a \)[/tex], we can add Equation (1) and Equation (2) together. This method works because the coefficients of [tex]\( a \)[/tex] in the two equations are opposites.
3. Add the equations:
[tex]\[
\begin{align*}
(5a + 5b) + (-5a + 5b) &= 25 + 35 \\
0a + 10b &= 60 \\
10b &= 60
\end{align*}
\][/tex]
We have successfully eliminated the variable [tex]\( a \)[/tex].
4. Identify the resulting equation:
The resulting equation after elimination is [tex]\( 10b = 60 \)[/tex].
Thus, the equation you obtain when using elimination to solve the given system is [tex]\( 10b = 60 \)[/tex].
1. Write down the given system of equations:
[tex]\[
\begin{align*}
(1) & \quad 5a + 5b = 25 \\
(2) & \quad -5a + 5b = 35
\end{align*}
\][/tex]
2. Eliminate one of the variables:
To eliminate [tex]\( a \)[/tex], we can add Equation (1) and Equation (2) together. This method works because the coefficients of [tex]\( a \)[/tex] in the two equations are opposites.
3. Add the equations:
[tex]\[
\begin{align*}
(5a + 5b) + (-5a + 5b) &= 25 + 35 \\
0a + 10b &= 60 \\
10b &= 60
\end{align*}
\][/tex]
We have successfully eliminated the variable [tex]\( a \)[/tex].
4. Identify the resulting equation:
The resulting equation after elimination is [tex]\( 10b = 60 \)[/tex].
Thus, the equation you obtain when using elimination to solve the given system is [tex]\( 10b = 60 \)[/tex].
