# 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 x1, y1, such that replacing x with x1 and y with y1, both equations are verified. 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.  