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

In summary, the two problems can be solved by setting up an augmented matrix and applying Gaussian Elimination.
  • #1
haydenmwht
3
0
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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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:
  • #6
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
 

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

How do I solve a system of equations to find the values of x, y, and z?

To solve a system of equations, you must first write out all of the equations and variables in a neat and organized way. Then, you can use methods such as substitution, elimination, or graphing to find the values of x, y, and z that satisfy all of the equations in the system.

What is the purpose of solving a system of equations?

The purpose of solving a system of equations is to find the values of the variables that satisfy all of the equations in the system. This can be useful in many real-world situations, such as finding the intersection point of two lines or determining the solution to a system of linear equations.

Can a system of equations have more than one solution?

Yes, a system of equations can have one, infinite, or no solutions. If there is one unique set of values for the variables that satisfies all of the equations, then there is one solution. If there are multiple sets of values that satisfy the equations, then there are infinite solutions. If there are no sets of values that satisfy the equations, then there are no solutions.

What is the difference between a consistent and an inconsistent system of equations?

A consistent system of equations is one in which there exists at least one solution. This means that the equations in the system can be satisfied by some set of values for the variables. An inconsistent system of equations has no solutions, meaning that the equations cannot be satisfied by any set of values for the variables.

How can I check if my solution to a system of equations is correct?

To check if your solution is correct, you can substitute the values for the variables into each equation in the system and see if they satisfy all of the equations. If the equations are all satisfied, then your solution is correct. Additionally, you can graph the equations to visually confirm that the solution is correct.

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