how can i solve three equations with three unknowns?

Answer 1

use matrix-methods ... ( i don't want to describe verbally)

or:


subtract one of the equations from one of the others (multiply both sides of one of them so that you eliminate one of the unknowns ie "multiply to make the coefficients equal before subtracting".

repeat this process with another pair of the three equations, eliminating the same unknown.


now you will have two equations with two unknowns.

with these two equations, subtract one from a muliple of the other and you will have one equation in one unknown.

solve this one,

insert the determined valu into one of the "two unknown equations" and you can solve this.

take these two (now known) unknown values and plug them back into one of the original values and you're home free.

the "matrix method" is more mechanical, but results in less understanding...

your choice

Answer 2

You can use elimination to get rid of at least one of the variables. Then rewrite one of the equations so that you can substitute into another equation...solve for 1 variable. Then solve for another, and finally use substitution for final variable.

When working with three equations, remember that you can multiply or divide all the coefficients of one equation by any constant and the equation is still valid. Another trick is to rewrite all equations so that the variables are all on one side and all aligned.

If you do know matrices, find discriminant and then solve. Easier than substitution and elimination.

Hope that helps.

Answer 3

You first could desire to control the equations so as which you have 2 equations with 2 variables. upload (a million) and (2) to get 3x + 4z = -12 (call this (4)) upload (2) and (3) to get 5x - 2z = -40 six (call this (5)) Double the two aspects of (5) to get 10x - 4z = -ninety two, then upload this to (4) to get 13x = -104. Divide the two aspects by utilising 13 to grant you x = -8. Sub this in to (4) to grant you -24 + 4z = -12, then upload 24 to the two aspects to get 4z = 12, meaning that z = 3. you are able to now in simple terms sub those 2 values lower back into (a million) for -8 + 5y + 6 = 40 3 => 5y - 2 = 40 3 => 5y = 40 5 => y = 9. placed a number of those values into (2) to make beneficial: -sixteen - 40 5 + 6 = -fifty 5 This works, so which you recognize those values are suited suited!

Answer 4

Solve one of the equations for a single variable.

Plug that expression in for the variable in the other 2 equations.

Solve those equations simultaneously, and then plug in those values in the first equation to get the value of the remaining variable.

Answer 5

Your question is very broad.
How to solve them depends upon whether they are linear or non-linear or even transcendental. If they are linear, then solving by matrix means, elimination of variables, etc will work really well.
For non-linear equations, say three of them that each contain at least one unknown, need to solved independently.

Answer 6

It depends on how complicated the three equations are.

If they are 3 linear independent equations, you can always solve them by elimination or matrix operation.

If they are non-linear equations, most likely you have to seek numerical methods.

Answer 7

Use the Chinese method, more or less what Athiest described. Don't use substitution, Jim's method. Usually, substitution gets to be very error-prone if you have more than two equations and two unknowns.

Answer 8

You can use the elimination method, in which you eliminate one variable at a time in order to get the solutions.

Answer 9

write the 1st variable as function of the sec and third variable.
the 2nd var as function of the third var
the third var as function of some numbers only

give an example of these functions thatis easier to explain

Answer 10

You know you can use different methods like substitution method, cramer's rule, etc.