Solving a Linear System in Three Variables
Step 1:- Eliminate a variable. Use the elimination method to eliminate any variable from any two of the original equations. The result is an equation in two variables.
Step 2:- Eliminate the same variable again. Eliminate the same variable from any other two equations. The result is an equation in the same two variables as in Step 1.
Step 3:- Eliminate a different variable and solve. Use the elimination method to eliminate a second variable from the two equations in two variables that result from Steps 1 and 2. The result is an equation in one variable that gives the value of that variable.
Step 4:- Find a second value. Substitute the value of the variable found in Step 3 into either of the equations in two variables to find the value of the second variable.
Step 5 :- Find a third value. Use the values of the two variables from Steps 3 and 4 to find the value of the third variable by substituting into any of the original equations.
Step 6:- Check the solution in all of the original equations. Then write the solution set.