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Examples, videos, worksheets, solutions, and activities to help Algebra students learn how to solve systems of equations involving three variables.
Solving a System of Equations Involving 3 Variables
Using Elimination by Addition - Example 1
2x - y + z = 3
5x + 2y -
3z = 1
2x + y - z = 2
Solving a System of Equations Involving 3 Variables
Using Elimination by Addition - Example 2
x + 2y + z = 12
2x - 2y - z = 6
x + 2y - z = 2
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Solving a System of Equations Involving 3 Variables
Using Elimination by Addition - Example 3
4x - 4y + 8z = 20
8x + 4y - 4z = 4
12x - 8y - 12z = -40
Solving a Dependent System of Linear Equations involving 3 Variables
Dependent systems have infinitely many solutions.
Solve. If the system is dependent, let z = c and write the solutions in terms of c.
x + 2y + z = 0
3x + 2y -z = 4
-x + 2y + 3z = -4
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More Algebra Worksheets
Focusing on solving systems of equations with three variables, this assemblage of printable worksheets provides immense practice to high school students. Featured here are simultaneous equations to be solved using the substitution method, the elimination method, Cramer's rule, and involves reciprocal equations as well. Included here is a review section allowing students to use a method of their choice. Click on our free worksheets and kick-start practice!
Substitution Method
Express one variable in terms of the other and substitute until one equation with one variable is left. Solve for the variable and perform back substitution to find the value of the other two, in this batch of pdf worksheets.
Elimination Method
Pair-up the linear equations to eliminate one variable and form two new equations of 2 variables each. Find the value of one variable by eliminating the other. Substitute and find the other two unknown variables in each system of equations.
Cramer's Rule
Extract the coefficient, x, y and z matrices from the systems of equations. Find the determinant of each 3 x 3 matrix. Divide the determinant of the x, y and z matrices with the coefficient matrix to find the solution to each system of equations with 3 variables.
Solve using Any Method
Each printable worksheet in this unit of solving systems of equations offers eight sets of equations. High school students use their discretion to choose from the substitution method, elimination method or the Cramer's Rule to find the solution to the systems of equations involving 3 variables.
Solving Reciprocal Equations
Replace each fraction in the equation with a variable to convert the reciprocal equations into standard equations. Apply any method of your choice and determine the solution.