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Answer :
To solve the given system of equations using elimination, let's look at each equation:
1) [tex]\(5a + 5b = 25\)[/tex]
2) [tex]\(-5a + 5b = 35\)[/tex]
The goal is to eliminate one of the variables by adding or subtracting the equations. Here, we can add both equations together to eliminate the variable [tex]\(a\)[/tex]. Here's how it works step-by-step:
1. Add the equations:
- [tex]\( (5a + 5b) + (-5a + 5b) = 25 + 35 \)[/tex]
2. Simplify the left side:
- The [tex]\(5a\)[/tex] and [tex]\(-5a\)[/tex] cancel each other out, so you're left with:
[tex]\((5b + 5b)\)[/tex]
3. Simplify further:
- Combine the terms with [tex]\(b\)[/tex]:
[tex]\(10b = 60\)[/tex]
So, the resulting equation from using elimination is:
[tex]\[10b = 60\][/tex]
This equation allows you to easily solve for [tex]\(b\)[/tex], if needed, but the question here is only about the resulting equation.
1) [tex]\(5a + 5b = 25\)[/tex]
2) [tex]\(-5a + 5b = 35\)[/tex]
The goal is to eliminate one of the variables by adding or subtracting the equations. Here, we can add both equations together to eliminate the variable [tex]\(a\)[/tex]. Here's how it works step-by-step:
1. Add the equations:
- [tex]\( (5a + 5b) + (-5a + 5b) = 25 + 35 \)[/tex]
2. Simplify the left side:
- The [tex]\(5a\)[/tex] and [tex]\(-5a\)[/tex] cancel each other out, so you're left with:
[tex]\((5b + 5b)\)[/tex]
3. Simplify further:
- Combine the terms with [tex]\(b\)[/tex]:
[tex]\(10b = 60\)[/tex]
So, the resulting equation from using elimination is:
[tex]\[10b = 60\][/tex]
This equation allows you to easily solve for [tex]\(b\)[/tex], if needed, but the question here is only about the resulting equation.
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