Systems of Equations in Two and Three Variables Advanced Math Topics Mrs. Mongold

Solving Systems By Elimination Choose a variable and get the coefficients to be opposites, then add the equations and solve for remaining value. Plug answer back in for second solution.

Remember Always check you solutions in BOTH equations!! Answers should be written as ordered pair If a system has at least one solution it is consistent If a system has no solution it is inconsistent Dependent equations are when all the ordered pairs for one equation satisfy the other equation

Three Variables… same but different 3 Patterns for a solution 1- Consistent, when three planes have a single point in common or when three planes intersect in a line

Three Variables… same but different 3 Patterns for a solution 1- Consistent, when three planes have a single point in common or when three planes intersect in a line 2-Inconsistent, when three planes intersect at no common points

Three Variables… same but different 3 Patterns for a solution 1- Consistent, when three planes have a single point in common or when three planes intersect in a line 2-Inconsistent, when three planes intersect at no common points 3-Dependent, when three planes coincide at all points

To Solve 3 variable systems Use elimination or substitution methods to get a system with two variables and then follow the rules for two variable systems

Example

Example

Example

Homework    

Homework