Answer :
To solve the given system of equations using the elimination method, follow these steps:
The system of equations is:
1. [tex]\( 5a + 5b = 25 \)[/tex]
2. [tex]\( -5a + 5b = 35 \)[/tex]
The goal of the elimination method is to add or subtract the equations to eliminate one of the variables. Let's eliminate the variable [tex]\( a \)[/tex].
Step 1: Add the two equations together to eliminate [tex]\( a \)[/tex].
- Equation 1: [tex]\( 5a + 5b = 25 \)[/tex]
- Equation 2: [tex]\( -5a + 5b = 35 \)[/tex]
Add these two equations:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
Step 2: Simplify the resulting equation.
When you add the left-hand sides of the equations, the [tex]\( a \)[/tex] terms ([tex]\( 5a \)[/tex] and [tex]\(-5a\)[/tex]) cancel each other out:
[tex]\[
5a - 5a + 5b + 5b = 10b
\][/tex]
Thus, the resulting equation is:
[tex]\[
10b = 60
\][/tex]
Therefore, using the elimination method, the resulting equation after eliminating [tex]\( a \)[/tex] is [tex]\( 10b = 60 \)[/tex].
The system of equations is:
1. [tex]\( 5a + 5b = 25 \)[/tex]
2. [tex]\( -5a + 5b = 35 \)[/tex]
The goal of the elimination method is to add or subtract the equations to eliminate one of the variables. Let's eliminate the variable [tex]\( a \)[/tex].
Step 1: Add the two equations together to eliminate [tex]\( a \)[/tex].
- Equation 1: [tex]\( 5a + 5b = 25 \)[/tex]
- Equation 2: [tex]\( -5a + 5b = 35 \)[/tex]
Add these two equations:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
Step 2: Simplify the resulting equation.
When you add the left-hand sides of the equations, the [tex]\( a \)[/tex] terms ([tex]\( 5a \)[/tex] and [tex]\(-5a\)[/tex]) cancel each other out:
[tex]\[
5a - 5a + 5b + 5b = 10b
\][/tex]
Thus, the resulting equation is:
[tex]\[
10b = 60
\][/tex]
Therefore, using the elimination method, the resulting equation after eliminating [tex]\( a \)[/tex] is [tex]\( 10b = 60 \)[/tex].
