How Do You Solve a System with Variables and Constants?

In summary, the conversation discusses a system of equations to be solved using Cramer's rule, with the equations being linear in A1, A2, A3, and A4. It is mentioned that there are two nonlinear equations in the system, but upon further examination, it is clarified that the system is, in fact, linear. The conversation also includes a link to images of the attempted solution, and it is noted that one of the expressions for A3 is incorrect. Suggestions are given for how to fix this error, and it is agreed that the system is, in fact, linear.
  • #1
JaZZyCooL
7
0

Homework Statement


Solve the following system of equations

Homework Equations


A1 + A3 = 0
cA1 + A2 + A4 = 0
dA1 + cA2 + w^2 A3 = 1
dA2 + w^2A4 = 0

The Attempt at a Solution



https://imgur.com/YSG5oGN - Page 1
https://imgur.com/dGbccsE - Page 2
 
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  • #2
I checked with Mathematica. Your expressions for A2 and A4 are correct. Your expression for A3 is not.
 
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  • #3
kuruman said:
I checked with Mathematica. Your expressions for A2 and A4 are correct. Your expression for A3 is not.
Knowing that, the OP should be able to easily fix A1 and A3.
 
  • #4
scottdave said:
Knowing that, the OP should be able to easily fix A1 and A3.
I agree. This particular system lends itself to using Cramer's rule because of all the zeroes on the right hand side.
 
  • #5
JaZZyCooL said:

Homework Statement


Solve the following system of equations

Homework Equations


A1 + A3 = 0
cA1 + A2 + A4 = 0
dA1 + cA2 + w^2 A3 = 1
dA2 + w^2A4 = 0

The Attempt at a Solution



https://imgur.com/YSG5oGN - Page 1
https://imgur.com/dGbccsE - Page 2
Here is your Page 1:
YSG5oGN.jpg


Here is your Page 2:
dGbccsE.jpg
 

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  • #6
the system shows two nonlinear equations. Not linear system.
 
  • #7
symbolipoint said:
the system shows two nonlinear equations. Not linear system.
The system is linear in A1, A2, A3, and A4 .
 
  • #8
SammyS said:
The system is linear in A1, A2, A3, and A4 .
These two equations are shown in the system:
dA1 + cA2 + w^2 A3 = 1
dA2 + w^2A4 = 0
Not linear. That shows an exponent of 2 on the w. If I misunderstand, then w is not a variable; but A1, A2, and A3 must be the variables. If this latter is the case, then yes; linear system.
 

1. What is a system of linear equations?

A system of linear equations is a set of two or more equations with multiple variables that need to be solved simultaneously.

2. How do I solve a system of linear equations?

There are several methods to solve a system of linear equations, including substitution, elimination, and graphing. Choose the method that works best for the given equations and follow the steps to solve for the variables.

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

Yes, a system of linear equations can have one, infinite, or no solutions. This depends on the relationship between the equations and the variables.

4. What is the importance of solving systems of linear equations?

Solving systems of linear equations is important in many fields, including mathematics, physics, engineering, and economics. It allows us to find the values of unknown variables and make predictions and decisions based on the relationships between the equations.

5. Can I use a calculator to solve a system of linear equations?

Yes, you can use a graphing calculator or online solver to solve a system of linear equations. However, it is important to understand the steps and methods involved in solving the equations, rather than relying solely on technology.

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