Solve System of Equations: Find x, y, z & l1, l2, l3

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SUMMARY

This discussion focuses on solving systems of equations using the Gaussian Elimination method. The first system consists of three equations: x + y + z = 15, 5x - z = 18, and 4y + z = 19, with the solution being x = 5, y = 3, and z = 7. The second system involves three variables l1, l2, and l3, represented by the equations l1 + l3 = l2, 5.2l1 - 3.25l2 = -12.35, and 3.25l2 - 2.61l3 = 64.35, yielding l1 = 17A, l2 = 31A, and l3 = 14A. The discussion emphasizes the use of augmented matrices and elementary row operations in Gaussian Elimination.

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haydenmwht
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I am new to this site and am not all that great at math but am trying to grow. I can't figure out how to work these equations.1) x + y + z = 15
5x - z = 18
4y + z = 19In this one I need to solve for the variables. the answers for x, y, z are 5,3,7

2) l1 + l3 = l2
5.2l1 - 3.25l2 = (-12.35)
3.25l2 - 2.61l3 = 64.35The answers for l1, l2, & l3 are 17A, 31A, & 14A. Thanks for any help!
 
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haydenmwht said:
I am new to this site and am not all that great at math but am trying to grow. I can't figure out how to work these equations.1) x + y + z = 15
5x - z = 18
4y + z = 19In this one I need to solve for the variables. the answers for x, y, z are 5,3,7

2) l1 + l3 = l2
5.2l1 - 3.25l2 = (-12.35)
3.25l2 - 2.61l3 = 64.35The answers for l1, l2, & l3 are 17A, 31A, & 14A. Thanks for any help!

There are many ways to solve these problems, and unless you show us what you have tried, we have no way of knowing which method is appropriate for the purposes of your course.
 
I am trying to use the Gaussian Elimination method but I am struggling in the exact steps going through them. I don't mean to sound dumb.
 
I am mainly struggling with problem 2. I found this in an Electricians Book and am confused on the steps for their answer. I'll figure it out soon I'm sure but am still confused.
 
Hi haydenmwht,

Both problems can be done by setting up an augmented matrix and applying Gaussian Elimination. I'm assuming you are confused about the process of applying GE? From wikipedia, the elementary row operations are the following:

  • Type 1: Swap the positions of two rows.
  • Type 2: Multiply a row by a nonzero scalar.
  • Type 3: Add to one row a scalar multiple of another.

There are no hard and fast rules to GE...just some better or worse methods. :)
 
Last edited:
Hi everyone,

I just wanted to point out in order to prevent any duplication of effort, that this question has been answered elsewhere.

Help with Problem - Math Help Forum
 

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