**Solving Equations Systems**

To solve equations systems in algebraic way, we have to end up to an equation that has only one unknown variable. To do this, we can add two equations together to zero out unknown variables or we can substitute a variable from one equation to another.

This technique will be explained by the following example:

Multiply the first equation by 3 and the second by -5:

Add the second equation to the first:

Multiply the second equation by 6 and the third by 15:

Add the third equation to the second:

Solve the second equation for x_{2}:

Substitute the second equation to the first:

From the first equation we get x_{3}=1. Substituting x_{3} to the second we get x_{2}=-4 and form the third we get x_{1}=3.

So the solution of the equations system using the algebraic way of solving it is: