System of Equations

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

System of Equations

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.

System of Equationsx = 2, y = 3

System of Equations Solution

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.

Linear Systems 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.

Linear Systems 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.

Linear Systems 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.

Equivalent Linear Systems

Equivalent Linear Systems

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

Equivalent Linear Systems

Equivalent Linear Systems