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Answer :
To solve this system of equations using the elimination method, we want to eliminate one of the variables by adding or subtracting the equations.
Here's the given system of equations:
1. [tex]\( 5a + 5b = 25 \)[/tex]
2. [tex]\( -5a + 5b = 35 \)[/tex]
Steps for elimination:
1. Add the two equations together to eliminate the variable [tex]\(a\)[/tex]:
- Equation 1: [tex]\( 5a + 5b = 25 \)[/tex]
- Equation 2: [tex]\( -5a + 5b = 35 \)[/tex]
When you add these two equations:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
2. Combine like terms:
- The terms [tex]\(5a\)[/tex] and [tex]\(-5a\)[/tex] cancel each other out.
- Combine the [tex]\(b\)[/tex] terms: [tex]\(5b + 5b = 10b\)[/tex].
So the equation becomes:
[tex]\[
10b = 60
\][/tex]
Therefore, the resulting equation when using elimination is [tex]\(10b = 60\)[/tex].
Here's the given system of equations:
1. [tex]\( 5a + 5b = 25 \)[/tex]
2. [tex]\( -5a + 5b = 35 \)[/tex]
Steps for elimination:
1. Add the two equations together to eliminate the variable [tex]\(a\)[/tex]:
- Equation 1: [tex]\( 5a + 5b = 25 \)[/tex]
- Equation 2: [tex]\( -5a + 5b = 35 \)[/tex]
When you add these two equations:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
2. Combine like terms:
- The terms [tex]\(5a\)[/tex] and [tex]\(-5a\)[/tex] cancel each other out.
- Combine the [tex]\(b\)[/tex] terms: [tex]\(5b + 5b = 10b\)[/tex].
So the equation becomes:
[tex]\[
10b = 60
\][/tex]
Therefore, the resulting equation when using elimination is [tex]\(10b = 60\)[/tex].
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