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Answer :
Sure! Let's solve the system of equations using the elimination method step by step.
We are given 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. Let's try eliminating the variable [tex]\(a\)[/tex].
### Step-by-step Solution:
1. Add the Equations:
We will add the two given equations together:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
2. Simplify the Expression:
When we add them, the [tex]\(5a\)[/tex] and [tex]\(-5a\)[/tex] terms will cancel each other out because they are equal but opposite in sign.
So, the equation simplifies to:
[tex]\[
0a + 10b = 60
\][/tex]
3. Resulting Equation:
This reduces to:
[tex]\[
10b = 60
\][/tex]
From this process, we can see that the resulting equation when using elimination to solve the given system is [tex]\(10b = 60\)[/tex]. That's the equation obtained after eliminating the variable [tex]\(a\)[/tex].
We are given 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. Let's try eliminating the variable [tex]\(a\)[/tex].
### Step-by-step Solution:
1. Add the Equations:
We will add the two given equations together:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
2. Simplify the Expression:
When we add them, the [tex]\(5a\)[/tex] and [tex]\(-5a\)[/tex] terms will cancel each other out because they are equal but opposite in sign.
So, the equation simplifies to:
[tex]\[
0a + 10b = 60
\][/tex]
3. Resulting Equation:
This reduces to:
[tex]\[
10b = 60
\][/tex]
From this process, we can see that the resulting equation when using elimination to solve the given system is [tex]\(10b = 60\)[/tex]. That's the equation obtained after eliminating the variable [tex]\(a\)[/tex].
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