Solving Simultaneous Equations: A Guide for Homework Assignments

In summary, the conversation discusses different methods to solve a system of simultaneous equations, specifically mentioning using a matrix or row-reduction and using cross multiplication. The conversation also suggests a specific approach of dividing all equations by 40, solving for one variable, and then plugging in the solution to solve for the remaining variables.
  • #1
JFonseka
117
0

Homework Statement



It's been a while since I solved these kind of things. I can only remember how to solve 2 simultaneous equations

40x + 40y = 10
-40y -40z = -2
40x - 40z = 8

Homework Equations



None

The Attempt at a Solution


Just need a pointer on what method to use.
 
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  • #2
You can put them in a matrix or row-reduce. But since the coefficients are very much alike, you can also try to do it more efficiently.
For example, you can use the latter two to eliminate z and then solve the remaining system of two. Then plug the solutions back into either of the last ones, and find z.
 
  • #3
1) Divide all by 40. (This should simplify alot)
2) Solve for y in terms of x (first equation)
3) Plug in for y (from equation 1) in the second equation, and solve for x. (Your y is in terms of x, so this should be easy)
4) Now, plug in the x that you found in the second equation (in terms of z), into the last equation. You'll find z. From there it's easy.

And of course, this is just one of the many ways to do it in this method.
 
  • #4
Use cross multiplication method.
 

1. What is a simultaneous equation?

A simultaneous equation is a set of two or more equations that have multiple variables and must be satisfied at the same time.

2. How do you solve a system of simultaneous equations?

To solve a system of simultaneous equations, you can use different methods such as substitution, elimination, or graphing. These methods involve manipulating the equations in order to find the values of the variables that satisfy all of the equations simultaneously.

3. What is the importance of simultaneous equations in science?

Simultaneous equations are important in science because they allow us to model real-world situations and make predictions. They are used in fields such as physics, engineering, and economics to understand and solve complex systems of equations.

4. What are some real-world applications of simultaneous equations?

Simultaneous equations have many real-world applications, including calculating the optimal production levels in a manufacturing process, determining the intersection points of two moving objects, and finding the equilibrium point in a chemical reaction.

5. Can simultaneous equations have more than two variables?

Yes, simultaneous equations can have any number of variables. However, the more variables there are, the more complex the system becomes and the more difficult it may be to solve. In some cases, it may be necessary to use advanced methods such as matrices or software programs to solve simultaneous equations with multiple variables.

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