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Answer :
Consider 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 using the elimination method.
1. To eliminate [tex]$a$[/tex], add equations (1) and (2) together. Adding the left-hand sides and the right-hand sides gives:
[tex]$$
(5a + 5b) + (-5a + 5b) = (25 + 35)
$$[/tex]
2. Notice that when we add the coefficients of [tex]$a$[/tex]:
[tex]$$
5a + (-5a) = 0a
$$[/tex]
And when we add the coefficients of [tex]$b$[/tex]:
[tex]$$
5b + 5b = 10b
$$[/tex]
Similarly, add the right-hand sides:
[tex]$$
25 + 35 = 60
$$[/tex]
3. The resulting equation is:
[tex]$$
0a + 10b = 60 \quad \Longrightarrow \quad 10b = 60
$$[/tex]
Thus, the resulting equation when elimination is used is:
[tex]$$
10b = 60.
$$[/tex]
[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 using the elimination method.
1. To eliminate [tex]$a$[/tex], add equations (1) and (2) together. Adding the left-hand sides and the right-hand sides gives:
[tex]$$
(5a + 5b) + (-5a + 5b) = (25 + 35)
$$[/tex]
2. Notice that when we add the coefficients of [tex]$a$[/tex]:
[tex]$$
5a + (-5a) = 0a
$$[/tex]
And when we add the coefficients of [tex]$b$[/tex]:
[tex]$$
5b + 5b = 10b
$$[/tex]
Similarly, add the right-hand sides:
[tex]$$
25 + 35 = 60
$$[/tex]
3. The resulting equation is:
[tex]$$
0a + 10b = 60 \quad \Longrightarrow \quad 10b = 60
$$[/tex]
Thus, the resulting equation when elimination is used is:
[tex]$$
10b = 60.
$$[/tex]
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