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Answer :
To solve the given system of equations using the elimination method, follow these steps:
We have the system of equations:
1. [tex]\( 5a + 5b = 25 \)[/tex]
2. [tex]\( -5a + 5b = 35 \)[/tex]
The goal of the elimination method is to eliminate one of the variables by adding or subtracting the equations. Here, we can add these two equations to eliminate the variable [tex]\( a \)[/tex].
Step 1: Add the two equations together.
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
By adding, the terms with [tex]\( a \)[/tex] cancel each other out because [tex]\( 5a + (-5a) = 0 \)[/tex].
This simplifies to:
[tex]\[
0a + 10b = 60
\][/tex]
Step 2: Simplify the equation.
Since [tex]\( 0a \)[/tex] doesn't contribute anything, the equation is simplified to:
[tex]\[
10b = 60
\][/tex]
Therefore, the resulting equation after using elimination is:
[tex]\[
10b = 60
\][/tex]
We have the system of equations:
1. [tex]\( 5a + 5b = 25 \)[/tex]
2. [tex]\( -5a + 5b = 35 \)[/tex]
The goal of the elimination method is to eliminate one of the variables by adding or subtracting the equations. Here, we can add these two equations to eliminate the variable [tex]\( a \)[/tex].
Step 1: Add the two equations together.
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
By adding, the terms with [tex]\( a \)[/tex] cancel each other out because [tex]\( 5a + (-5a) = 0 \)[/tex].
This simplifies to:
[tex]\[
0a + 10b = 60
\][/tex]
Step 2: Simplify the equation.
Since [tex]\( 0a \)[/tex] doesn't contribute anything, the equation is simplified to:
[tex]\[
10b = 60
\][/tex]
Therefore, the resulting equation after using elimination is:
[tex]\[
10b = 60
\][/tex]
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