# System of Equations

Two equations with two unknowns form a system if they have a common solution

The solution of a system is a pair of numbers *x _{1}*

_{, }

*, such that replacing*

**y**_{1}**with**

*x***and**

*x*_{1}**with**

*y***, both equations are verified.**

*y*_{1}x = 2, y = 3

## Properties of Linear Systems

1. If both members of an equation in a system are added or subtracted by the same expression, the resulting system is equivalent.

x = 2, y = 3

2.If both members of the equations of a system are multiplied or divided by a nonzero number, the resultant system is equivalent.

x = 2, y = 3

3. If an equation of a system is added or subtracted by another equation of the same system, the resultant system is equivalent.

x = 2, y = 3

4.If in a system, an equation is replaced by another equation that is obtained from adding the two equations from a system previously multiplied or divided by a nonzero number, the resultant system is equivalent.

5. If the order of the equations or the order of the unknowns changes, it is another equivalent system.