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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
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# Graphing Equations in Three Variables

Example

An inconsistent system of three linear equations

Solve the system:

 (1)(2) (3) x3x 2x +- + y2y 2y -+ - zz 2z = 5= 8 = 7

Solution

We can eliminate the variable z from Eqs. (1) and (2) by adding them:

 (1)(2) x3x +- y2y -+ zz = 5= 8 4x - y = 13

To eliminate z from Eqs. (1) and (3), multiply Eq. (1) by 2 and add the resulting equation to Eq. (3):

 -2x3x -+ 2y2y +- 2z2z = -10= 7 Eq. (1) multiplied by -2Eq. (3) 0 = -3

Because the last equation is false, there are two inconsistent equations in the system. Therefore the solution set is the empty set.