Answer :
To solve the given system of equations using the elimination method, we want to eliminate one of the variables, either [tex]\( a \)[/tex] or [tex]\( b \)[/tex]. Here are the steps:
Given system of equations:
1. [tex]\( 5a + 5b = 25 \)[/tex]
2. [tex]\(-5a + 5b = 35\)[/tex]
Step 1: Add the two equations together
When we add the equations, the [tex]\( a \)[/tex] terms will cancel each other out because [tex]\( 5a \)[/tex] and [tex]\(-5a\)[/tex] add up to 0:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
Step 2: Simplify the resulting equation
After adding, we simplify the equation:
[tex]\[
5a - 5a + 5b + 5b = 60
\][/tex]
This simplifies to:
[tex]\[
0a + 10b = 60
\][/tex]
So, the resulting equation after elimination is:
[tex]\[
10b = 60
\][/tex]
Therefore, the correct resulting equation when elimination is used is [tex]\( 10b = 60 \)[/tex].
Given system of equations:
1. [tex]\( 5a + 5b = 25 \)[/tex]
2. [tex]\(-5a + 5b = 35\)[/tex]
Step 1: Add the two equations together
When we add the equations, the [tex]\( a \)[/tex] terms will cancel each other out because [tex]\( 5a \)[/tex] and [tex]\(-5a\)[/tex] add up to 0:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
Step 2: Simplify the resulting equation
After adding, we simplify the equation:
[tex]\[
5a - 5a + 5b + 5b = 60
\][/tex]
This simplifies to:
[tex]\[
0a + 10b = 60
\][/tex]
So, the resulting equation after elimination is:
[tex]\[
10b = 60
\][/tex]
Therefore, the correct resulting equation when elimination is used is [tex]\( 10b = 60 \)[/tex].
