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Simultaneous equations in three variables
By Lesley Mcgill on Sunday, September 09, 2001 - 04:12 pm:

I have a complete memory block when it comes to three variable equations. I get past the first step of eliminating a variable then get totally lost and confused.

Can you explain this to me in easy steps.

u-2v+w=0
3u+ 4v+2w=17
4u-3v+2w=4

Thanks

By Arun Iyer on Sunday, September 09, 2001 - 07:33 pm:

For your example........
Let,
u-2v+w=0 .......(1)
3u+ 4v+2w=17 ...(2)
4u-3v+2w=4 .....(3)

FIRST, multiply eqn 1 by 2 and then subtract eqn 1 from say eqn 3. You will get a equation in two variables namely u and v. Let it be eqn 4.

SECOND, subtract eqn 2 from say eqn 3. You will get again a equation in two variables. Let it be eqn 5.

Solve eqn 4 and eqn 5 and get u and v.
Substituting these values of u and v in any of eqn 1,2,3, you will get w.

Question solved.

Summary:

  1. I have eliminated a variable and got two equations with two variables.
  2. I solved the two newly found equations simultaneously and got the two unknowns.
  3. I substituted these values in one of the original equations to get the value of the third variable.

love arun