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Systems of Equations with Three Variables | Simultaneous Equations Worksheets

Focusing on solving systems of equations with three variables, this assemblage of 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.

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 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 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.

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