Solving the example, hope it will help you with better understanding.
Given system:
We need to eliminate one of the variables c or d. Let us eliminate d.
We see the first equation has 3d and the second equation has - d. The coefficients of d are 3 and - 1. If we multiply the second one by 3 it will become - 3, then if we add them up they will cancel, 3d - 3d = 0. By doing this we'll eliminate the variable d and left with variable c in the resulting equation.
Demonstrating how it works:
2c + 3d = 12, we leave it as is
5c - d = 13, we multiply all terms of this by 3, it becomes, 15c - 3d = 39
Now add up the two equations:
- 2c + 15c + 3d - 3d = 12 + 39, eliminated d
- 17c = 51 solving for c
- c = 51/17
- c = 3
Now we can find the value of d:
- 2c + 3d = 12
- 2*3 + 3d = 12
- 6 + 3d = 12
- 3d = 6
- d = 2
Our solution is:
