This is a free lesson from our course in Algebra II
In this section, you'll learn the method of solving system of equations in three variables by substitution.
This method for solving this system is analogous to the methods used to solve the
two variable systems.To solve a system in three variables, it must
have three different equations which relate the unknowns. Explaination is provided with the help of some examples presented with
video, in instructor's voice and own handwriting to how to solve the system of equations which will clear the concept in detail.
(More text below video...)
(Continued from above) Procedure:
Let, we have three equations equation 1, equation 2, and equation 3 having variables x, y, and z. The substitution method has these basic steps:
• solve equation1 for z.
• substitute the whole righthand side of the equation (the one you just wrote) in place of "z" in equation 2. You should use parentheses around the substituted expression to keep everything orderly.
• solve the equation you wrote in step 2 for y.
• substitute the whole righthand side of the equation you wrote in step 1 in place of "z" in equation3. Then substitute the whole righthand side of the equation you wrote in step 3 in place of "y" in equation 3.
• solve the equation you wrote in step 4 for x. You should get a numeric value of x.
• use this value of x in the equation you wrote in step 3 to solve for y. You should get a numeric value of y.
• use these values of x and y in the equation you wrote in step 1 to solve for z.
You should get a numeric value of z. For example, the system
of equations x + y + z = 6, 3x + 2y
+ z = 10, and 2x + 4y + 3z = 19, simplifies and
yields to x = 1, y = 2 and z = 3.
Winpossible's online math courses and tutorials have gained rapidly popularity since
their launch in 2008. Over 100,000 students have benefited from Winpossible's courses...
these courses in conjunction with free unlimited homework help serve as a very effective
mathtutor for our students.

All of the Winpossible math tutorials have been designed by topnotch instructors
and offer a comprehensive and rigorous math review of that topic.

We guarantee that any student who studies with Winpossible, will get a firm grasp
of the associated problemsolving techniques. Each course has our instructors providing
stepbystep solutions to a wide variety of problems, completely demystifying the
problemsolving process!

Winpossible courses have been used by students for help with homework and by homeschoolers.

Several teachers use Winpossible courses at schools as a supplement for inclass
instruction. They also use our course structure to develop course worksheets.