Solving Systems of Three Equations with Three Unknowns

Tutoring on Solving Systems of Three Equations with Three Unknowns

Learning Objectives:

Understand to Solve Systems of Three Equations with Three Unknowns.

Math Tutoring on Solving Systems of Three Equations with Three Unknowns

To solve this system of equations there are three different ways:   

 1) Substitution,   2) Elimination,    3) Matrices.   

The process of substitution involves several steps:  

Step 1: Solve for one of the variables in one of the equations. It makes no difference which equation and which variable you choose. Let us solve for x in equation (1). 

Step 2: Substitute this value for x in equations (2) and (3). This will change equations (2) and (3) to equations in the two variables y and z. Call the changed equations (4) and (5), respectively.  

Step 3: Solve for y in equation (5). 

Step 4: Substitute this value of y in equation (4). This will give you an equation in z. Solve for z. 

Step 5: Substitute this value of z in equation (6) and solve for y. 

Step 6: Substitute for y and z in equation (1) and solve for x. 

The process of elimination involves several steps: 

First, reduce three equations to two equations with two variables, and then to one equation with one variable. The process of using matrices is essentially a shortcut of the process of elimination. Each row of the matrix represents an equation and each column represents coefficients of one of the variables.

 

 

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Hook Questions:

1.    What are the three methods to solve the system of three equations with three unknowns?

2.    Which method is most convenient and why?

3.    Can you solve the system of equations involving more than three unknowns?

 

 

 

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