Math Questions?

Question

I'm asking about "two" things:

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!

Answer 1

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.html

Answer 2

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.