Given three equation and three unknown
Step 1. Eliminate one unknown from first two equations. Let us take
Subtracting (2) from (1) we get
Step 2. Eliminate same unknown from next two equations. (one can choose last two as well).
Multiplying (2) with
We now have two equations (4) and (5) with two unknowns.
Step 3. Eliminate one unknown from these two equations.
We see that if we add these two we eliminate
Step 4. Insert this value of
Step 5. Insert these values of