Answer :
We start with the system of equations:
[tex]$$
\begin{aligned}
5a + 5b &= 25 \quad \text{(1)}\\
-5a + 5b &= 35 \quad \text{(2)}
\end{aligned}
$$[/tex]
Our goal is to eliminate one of the variables by adding the two equations together. Notice that by adding (1) and (2), the [tex]$a$[/tex]-terms cancel out:
[tex]$$
(5a + 5b) + (-5a + 5b) = 25 + 35.
$$[/tex]
Simplify the left-hand side:
[tex]$$
5a - 5a + 5b + 5b = 0 + 10b = 10b.
$$[/tex]
And simplify the right-hand side:
[tex]$$
25 + 35 = 60.
$$[/tex]
Thus, we obtain the equation:
[tex]$$
10b = 60.
$$[/tex]
This is the resulting equation after the elimination step.
[tex]$$
\begin{aligned}
5a + 5b &= 25 \quad \text{(1)}\\
-5a + 5b &= 35 \quad \text{(2)}
\end{aligned}
$$[/tex]
Our goal is to eliminate one of the variables by adding the two equations together. Notice that by adding (1) and (2), the [tex]$a$[/tex]-terms cancel out:
[tex]$$
(5a + 5b) + (-5a + 5b) = 25 + 35.
$$[/tex]
Simplify the left-hand side:
[tex]$$
5a - 5a + 5b + 5b = 0 + 10b = 10b.
$$[/tex]
And simplify the right-hand side:
[tex]$$
25 + 35 = 60.
$$[/tex]
Thus, we obtain the equation:
[tex]$$
10b = 60.
$$[/tex]
This is the resulting equation after the elimination step.
