Solving system of linear equations

In summary, the conversation discusses solving a system of linear equations with three unknowns. The suggested methods include Cramer's rule and Gaussian elimination. However, it is also noted that the system can be simplified by eliminating y_3 and reducing it to a two equations in two unknowns problem.
  • #1
pinki82
9
0
Find/solve following system of linear equations,

3y_1 + 2y_2 +y_4 = 6
5y_1 - 2y_2 +2y_4 = 5
-2y_1 + y_2 - y_4 = -2



WORK DONE :

I am told that the answers are y_1 = 1 and y_2= 1 and y_4 = 1.
But i don't understand how to obtain these values...
I know how to solve 2 linear systerm of equations...but how do i solve
3 linear system of equations like the one above?
 
Physics news on Phys.org
  • #2
try cramers rule. are you familer with this
 
  • #3
How in the world did this get into differential equations? I'm going to move it.

There are a variety of ways of solving systems of equations. Cramer's rule, that mathmike mentions, is simple to set up but involves a lot of tedious calculation. I notice that if you add the first and third equations, y_3 is eliminated and if you subtract twice the third equation from the second, y_3 is again eliminated, leaving you with two equations in two unknowns. Find a way of eliminated either y_1 or y_2 from those two and you have just one equation in one unknown that should be easy to solve.
 
  • #4
If you have learned about matrices, you can solve this by using Gaussian elimination which basically comes down to what HallsofIvy illustrated with lineair combinations to eliminate certain unknowns out of one or more equations. With the subtle difference that in this way, you only work with the coefficients in a matrix and not explicitly with the system and all of its unknowns.
 

1. What is a system of linear equations?

A system of linear equations is a set of two or more equations that involve two or more variables and have a common solution. It is a mathematical representation of a real-world problem that can be solved to find the values of the variables.

2. Why is it important to solve systems of linear equations?

Solving systems of linear equations is important because it allows us to find the values of the variables that satisfy all the given equations simultaneously. This can help us make predictions, solve real-world problems, and make informed decisions.

3. What are the different methods for solving systems of linear equations?

The most commonly used methods for solving systems of linear equations are substitution, elimination, and graphing. Other methods include matrices, determinants, and Gaussian elimination.

4. How do you know if a system of linear equations has a solution?

A system of linear equations has a solution if the equations are consistent, meaning they have at least one common solution, or if they are inconsistent, meaning they have no common solution. This can be determined by looking at the number of solutions and the number of equations in the system.

5. Can a system of linear equations have more than one solution?

Yes, a system of linear equations can have one, infinite, or no solution. If the number of equations is less than the number of variables, the system will have infinite solutions. If the number of equations is equal to the number of variables, the system will have a unique solution. If the equations are inconsistent, the system will have no solutions.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
6
Views
532
  • Precalculus Mathematics Homework Help
Replies
5
Views
719
  • Calculus and Beyond Homework Help
Replies
5
Views
191
Replies
3
Views
619
  • Calculus and Beyond Homework Help
Replies
10
Views
407
  • Differential Equations
Replies
4
Views
1K
  • Precalculus Mathematics Homework Help
Replies
5
Views
940
  • Precalculus Mathematics Homework Help
Replies
4
Views
720
  • Precalculus Mathematics Homework Help
Replies
6
Views
1K
Replies
3
Views
1K
Back
Top