Solving Simultaneous Equations for Homework Assignments

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Homework Help Overview

The discussion revolves around solving a set of three simultaneous equations involving three variables: x, y, and z. Participants are exploring methods to approach the problem, which includes considerations of simplification and elimination techniques.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various methods such as matrix row-reduction, elimination of variables, and simplification by dividing coefficients. There are suggestions to express one variable in terms of another and to use cross multiplication.

Discussion Status

The discussion is active, with multiple methods being proposed for solving the equations. Some participants provide specific steps while others suggest general strategies. There is no explicit consensus on a single approach, indicating a variety of perspectives being explored.

Contextual Notes

Participants note the similarity of coefficients in the equations, which may influence the choice of method. There is also a mention of the original poster's uncertainty due to a lack of recent practice with such problems.

JFonseka
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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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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.
 
1) Divide all by 40. (This should simplify a lot)
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.
 
Use cross multiplication method.
 

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