Solving Simultaneous Equations: Methods and Accuracy

In summary, the speaker discusses their experience with solving simultaneous equations in different ways and obtaining different answers for x. They mention using Mathematica to solve the equations and getting x=1.0472, which is equivalent to 60 degrees. However, when they submitted this answer for an engineering assignment, they were told the correct answer for x was 60 degrees. They then tried another method, equating both equations and solving for t with x=60, and obtained a slightly different answer of 49.476. The speaker questions why these two methods yielded different values for x and how they can determine which one is correct.
  • #1
Ry122
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[SOLVED] simultaneous equations

Why is it that when solving some simultaneous equations two different ways you can get two different answers? One example is this:
0=-tsin(x)+85.7sin(30) eq. 1
0=-tcos(x)+85.7cos(30)-t eq. 2
I solved these equations in mathematica and got t=49.4789 and x=1.0472. These were the values I submitted for an engineering assignment I recently had and I only got t correct, the correct answer for x was 60 degrees.
So knowing which value was correct i subbed it into eq1. and i still got x=1.04723
Then I tried using a different method. I equated both equations so eq1=eq2 and i used x=60 to solve for t and i got 49.476. Why did these two different methods yield two different values for x and how am I supposed to know which one is correct?
 
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  • #2
Using mathematica to solve the equations may not be helping you understand them. In the answer x=1.0472, x is expressed in radians. That IS 60 degrees.
 

FAQ: Solving Simultaneous Equations: Methods and Accuracy

1. What are simultaneous equations?

Simultaneous equations are a set of equations that are solved together. They contain two or more variables and each equation has the same variables.

2. How do you solve simultaneous equations?

The most common method for solving simultaneous equations is the elimination method. This involves manipulating the equations to eliminate one of the variables and then solving for the remaining variable.

3. What is the difference between consistent and inconsistent simultaneous equations?

Consistent simultaneous equations have at least one set of values that satisfy all the equations. Inconsistent simultaneous equations have no solution that satisfies all the equations.

4. Can you use substitution to solve simultaneous equations?

Yes, substitution is another method for solving simultaneous equations. It involves solving one equation for a variable, and then substituting that expression into the other equation to solve for the remaining variable.

5. Why are simultaneous equations important in science?

Simultaneous equations are important in science because they allow us to represent and solve real-world problems involving multiple variables. They are used in fields such as physics, engineering, and chemistry to model and analyze complex systems.

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