Solving System of Equations Using Matrices

In summary, there are four solutions to the system of equations given, with the x and y values listed above. Matrices are not applicable in this case as they are used for linear systems of equations.
  • #1
GreenPrint
1,196
0

Homework Statement


Is it possible to solve this system of equations using matrices?
x^2 + y^2 = 42
x+3y+2y^2=6

Homework Equations





The Attempt at a Solution


I solved the system of equations using the following MATLAB code. I'm kind of confused by the results. Are there two x values and two y values? I don't know how to interpret what it says x and y are equal to. Thanks in advance.

Code: 
>>one=sym('x^2+y^2-42');
two=sym('x+3*y+2*y^2-6');
[x,y]=solve(one,two)
 
x =
 
 -6.2161908711674029137999766546085
  6.4782037201238076694174751205659
  6.3321946913754454971273459117746
  -5.594207540331850252744844377732
 
 
y =
 
   1.8327495882457713513416277757555
 -0.18131894709064188368251606877471
  -1.3796051574695662000556283784362
  -3.2718254836855632676034833285446
 
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  • #2
GreenPrint said:
Is it possible to solve this system of equations using matrices?

x^2 + y^2 = 42
x+3y+2y^2=6

No, matrices are applied to linear systems of equations.

GreenPrint said:

The Attempt at a Solution


I solved the system of equations using the following MATLAB code. I'm kind of confused by the results. Are there two x values and two y values? I don't know how to interpret what it says x and y are equal to. Thanks in advance.

There are four solutions: (x,y) pairs

x=-6.216 and y=1.832,
x=6.478 and y=-0.181 and so on.

ehild
 

FAQ: Solving System of Equations Using Matrices

1. What is a system of equations?

A system of equations is a set of two or more equations that contain the same variables. The goal is to find the values of the variables that satisfy all of the equations simultaneously.

2. How can matrices be used to solve a system of equations?

Matrices can be used to represent the coefficients and constants in the system of equations. By performing operations on the matrices, such as row operations and Gaussian elimination, the system of equations can be solved.

3. What is the advantage of using matrices to solve a system of equations?

Using matrices can simplify the process of solving a system of equations, especially when there are a large number of equations and variables. It also allows for a more organized and systematic approach to solving the system.

4. Can all systems of equations be solved using matrices?

No, not all systems of equations can be solved using matrices. Some systems may have no solution, while others may have infinitely many solutions. Matrices can only be used to solve systems of equations that have a unique solution.

5. Are there any limitations to using matrices to solve a system of equations?

One limitation is that matrices can become very large and complex when solving systems with a large number of equations and variables. Additionally, round-off errors can occur when performing operations on matrices, which can affect the accuracy of the solution.

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