Problem 44 - College Algebra Essentials

Question

Describe in general terms how to solve a system in three variables.

Step-by-Step Solution

Answer

A system of three variables can be solved by arranging the system in a convenient way, then using the elimination method to get rid of one variable, isolating one variable, and substituting this into another pair of equations. The new pair is then solved using the elimination method. Afterwards, substitute the determined variables into any of the original equations. Finally, check the solution by substituting all the solved variables into all the original equations.

Step 1: Arrange Equations and Select Pair

Arrange the system in a convenient way. Then select any two equations of the system and discard the other temporarily.

Step 2: Elimination Method

Apply the elimination method to the selected pair of equations to eliminate one of the variables.

Step 3: Isolate one Variable

Re-arrange the result from step 2 to express one variable in terms of the other (Let's call it variable X).

Step 4: Substitution into Another Pair

Select another pair of equations, one of which must be the one discarded in step 1. Substitute X into this new pair of equations.

Step 5: Solve using Elimination Method

Solve the new pair of equation using the elimination method. This will result in getting another variable's value (Say variable Y).

Step 6: Substitute to Get Third Variable

Substitute X and Y (the determined variables) into any of the original equations of the system. This will result in solving for the third and last variable (Variable Z).

Step 7: Check Solution

Substitute all the solved variables (X, Y, Z) into all the original equations to check the correctness of the solution.