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Answer :
To solve the given system of equations using the elimination method, let's go through the steps:
The given system of equations is:
1. [tex]\(5a + 5b = 25\)[/tex]
2. [tex]\(-5a + 5b = 35\)[/tex]
Our goal is to eliminate one of the variables. In this case, let's eliminate the variable [tex]\(a\)[/tex].
To do this, we need to add the two equations together:
- Adding the left sides: [tex]\((5a + 5b) + (-5a + 5b)\)[/tex]
- Adding the right sides: [tex]\(25 + 35\)[/tex]
When we add the left sides:
- [tex]\(5a + (-5a) = 0a\)[/tex], so they cancel each other out.
- [tex]\(5b + 5b = 10b\)[/tex]
Thus, the resulting equation after adding the two left sides is:
[tex]\[0a + 10b = 60\][/tex]
Since [tex]\(0a\)[/tex] is just zero, we get:
[tex]\[10b = 60\][/tex]
This is the resultant equation when using elimination on the given system.
Therefore, the correct result from using the elimination method is:
[tex]\[10b = 60\][/tex]
The given system of equations is:
1. [tex]\(5a + 5b = 25\)[/tex]
2. [tex]\(-5a + 5b = 35\)[/tex]
Our goal is to eliminate one of the variables. In this case, let's eliminate the variable [tex]\(a\)[/tex].
To do this, we need to add the two equations together:
- Adding the left sides: [tex]\((5a + 5b) + (-5a + 5b)\)[/tex]
- Adding the right sides: [tex]\(25 + 35\)[/tex]
When we add the left sides:
- [tex]\(5a + (-5a) = 0a\)[/tex], so they cancel each other out.
- [tex]\(5b + 5b = 10b\)[/tex]
Thus, the resulting equation after adding the two left sides is:
[tex]\[0a + 10b = 60\][/tex]
Since [tex]\(0a\)[/tex] is just zero, we get:
[tex]\[10b = 60\][/tex]
This is the resultant equation when using elimination on the given system.
Therefore, the correct result from using the elimination method is:
[tex]\[10b = 60\][/tex]
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