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Answer :
To solve the given system of equations using the elimination method, follow these steps:
We have the 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. In this case, we can add the two equations to eliminate the variable [tex]\( a \)[/tex].
Let's add the equations:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
When we do this, the [tex]\( 5a \)[/tex] term and the [tex]\(-5a\)[/tex] term cancel each other out:
[tex]\[
0a + 10b = 60
\][/tex]
This simplifies to:
[tex]\[
10b = 60
\][/tex]
Therefore, the resulting equation when using elimination to solve the system is:
[tex]\[
10b = 60
\][/tex]
This new equation involves only the variable [tex]\( b \)[/tex], which is what we aimed to achieve using the elimination method.
We have the 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. In this case, we can add the two equations to eliminate the variable [tex]\( a \)[/tex].
Let's add the equations:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
When we do this, the [tex]\( 5a \)[/tex] term and the [tex]\(-5a\)[/tex] term cancel each other out:
[tex]\[
0a + 10b = 60
\][/tex]
This simplifies to:
[tex]\[
10b = 60
\][/tex]
Therefore, the resulting equation when using elimination to solve the system is:
[tex]\[
10b = 60
\][/tex]
This new equation involves only the variable [tex]\( b \)[/tex], which is what we aimed to achieve using the elimination method.
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