Answer :
To solve this system of equations using elimination, we start with the given equations:
1. [tex]\(5a + 5b = 25\)[/tex]
2. [tex]\(-5a + 5b = 35\)[/tex]
To eliminate the variable [tex]\(a\)[/tex], we can add the two equations together. Here's how that works step-by-step:
- Add the left sides of the equations together: [tex]\((5a + 5b) + (-5a + 5b)\)[/tex]
- Add the right sides of the equations together: [tex]\(25 + 35\)[/tex]
When we add the left sides, the [tex]\(5a\)[/tex] and [tex]\(-5a\)[/tex] cancel each other out, leaving:
[tex]\(5b + 5b = 10b\)[/tex]
On the right side, we add the numbers:
[tex]\(25 + 35 = 60\)[/tex]
So, the resulting equation after elimination is:
[tex]\(10b = 60\)[/tex]
This equation shows that [tex]\(b\)[/tex] is the variable left, and it simplifies the system to find [tex]\(b\)[/tex] easily.
1. [tex]\(5a + 5b = 25\)[/tex]
2. [tex]\(-5a + 5b = 35\)[/tex]
To eliminate the variable [tex]\(a\)[/tex], we can add the two equations together. Here's how that works step-by-step:
- Add the left sides of the equations together: [tex]\((5a + 5b) + (-5a + 5b)\)[/tex]
- Add the right sides of the equations together: [tex]\(25 + 35\)[/tex]
When we add the left sides, the [tex]\(5a\)[/tex] and [tex]\(-5a\)[/tex] cancel each other out, leaving:
[tex]\(5b + 5b = 10b\)[/tex]
On the right side, we add the numbers:
[tex]\(25 + 35 = 60\)[/tex]
So, the resulting equation after elimination is:
[tex]\(10b = 60\)[/tex]
This equation shows that [tex]\(b\)[/tex] is the variable left, and it simplifies the system to find [tex]\(b\)[/tex] easily.
