# Math Questions?

1-I don't get how to solve equations of 3variables!!!! does anyone have an easy way to solve it ? with an example!!

2-Does anyone have a link to "System Of Equations And Inqualities"??? I need a site with alot of exercises & solutions.

**5stars for the best answer! *Promise*!! :)

thnx!

Relevance

Solving Equations with 3 variables

Since you would need a three-dimensional coordinate system to solve systems in three variables, solving graphically is not an option. Substitution would work, but is usually unmanageable. Therefore, we will use the addition method, which is basically the same process as it is with systems in two variables.

1. Problem: Solve the following system:

x + y + z = 4

x - 2y - z = 1

2x - y - 2z = -1

Solution: Start out by multiplying the

first equation by -1 and add

it to the second equation to

eliminate x from the second

equation.

-x - y - z = -4

x - 2y - z = 1

----------------

-3y - 2z = -3

Now eliminate x from the third

equation by multiplying the first

equation by -2 and add it to

the third equation.

-2x - 2y - 2z = -8

2x - y - 2z = -1

------------------

-3y - 4z = -9

Next, eliminate y from the third

equation by multiplying the second

equation by -1 and adding it to

the third equation.

3y + 2z = 3

-3y - 4z = -9

--------------

-2z = -6

Solve the third equation for z.

-2z = -6

z = 3

Substitute 3 for z in the

second equation and solve for y.

-3y - 2z = -3

-3y - 2(3) = -3

-3y - 6 = -3

-3y = 3

y = -1

Lastly, substitute -1 for y and

3 for z in the first equation

and solve for x.

x + (-1) + 3 = 4

x + 2 = 4

x = 2

The answer is (2, -1, 3).

System of Equations and Inequalities Link:

http://library.thinkquest.org/20991/alg2/systems.h...

• Sharon gave a great example for solving the system. The only thing I can add to that is this: When working with three equations, pick any two equations and eliminate a variable. Then select the third equation and one of the first two and eliminate THE SAME VARIABLE. This is the key. When you do this, you reduce the system to two equations with two variables.