Answer :
To solve the given system of equations using the elimination method, we want to eliminate one of the variables by adding or subtracting the equations from each other.
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, so we'll start by adding the two equations together. Here's a step-by-step breakdown:
1. Write down both equations vertically, aligning the terms:
[tex]\[
\begin{array}{r}
5a + 5b = 25 \\
-5a + 5b = 35
\end{array}
\][/tex]
2. Add the corresponding sides of the two equations:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
3. Simplify the left side of the equation by combining like terms:
[tex]\[
(5a - 5a) + (5b + 5b) = 10b
\][/tex]
So it becomes:
[tex]\[
10b = 60
\][/tex]
After adding the equations, the resulting simplified equation is [tex]\(10b = 60\)[/tex]. This shows that the original system of equations, when eliminated of the variable [tex]\(a\)[/tex], leads to the equation [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, so we'll start by adding the two equations together. Here's a step-by-step breakdown:
1. Write down both equations vertically, aligning the terms:
[tex]\[
\begin{array}{r}
5a + 5b = 25 \\
-5a + 5b = 35
\end{array}
\][/tex]
2. Add the corresponding sides of the two equations:
[tex]\[
(5a + 5b) + (-5a + 5b) = 25 + 35
\][/tex]
3. Simplify the left side of the equation by combining like terms:
[tex]\[
(5a - 5a) + (5b + 5b) = 10b
\][/tex]
So it becomes:
[tex]\[
10b = 60
\][/tex]
After adding the equations, the resulting simplified equation is [tex]\(10b = 60\)[/tex]. This shows that the original system of equations, when eliminated of the variable [tex]\(a\)[/tex], leads to the equation [tex]\(10b = 60\)[/tex].
