How do you solve equations with 3 different variables?

Answer 1

THERE R EQN
N CAN BE SOLVED BY
MATRIX METHOD
SUBSTITUTING
GAUSS ELIMINATION
INVERSE MATRIX
THERE R A LOT OF THOSE

Answer 2

What are the equations you have? If you have 3 different equations, you can solve each one for one of the variables (so if you have x, y, z then solve one for x and plug it into a different equation. This should eliminate one of the variables if you did it right. Then you should have two variables left with only two equations, you should be able to plug one into the other resulting in one variable you can solve for. then you can go back and plug in the answer in for one of the variables)

Sorry if that's confusing, it is hard to explain without knowing the equations.

Answer 3

You systematically/methodically eliminate a particular variable from 2 different pair of equations. (This assumes you have the requisite 3 independent equations involving the 3 unknowns.)

That provides you with 2 equations in 2 unknowns (since you used 2 DIFFERENT pairs to eliminate 1 chosen variable).

You should be able to take it from there -- either solving for one of the remaining 2 variables be substitution; or repeating the first process(above) eliminating one of the remaining 2 variables.

Answer 4

For a start, it's generally a good idea to have at least three equations (though special cases exist, like x^2 + y^2 + x^2 = 0 for x, y, z real).

Anyway, thre are two basic method: substitution and elimination.

In the substitution method, use one equation to write one of the variables in terms of the other two. Substitute this expression into the other two equations so that they are written entirely in terms of the other two variables. Then pick one of those variables and repeat the process with the two new equations. This will get you an equation with one variable in it which you can solve. Then put this value into the expression for the second variable to find its value. Then put these two values into the expression for the first variable to find its value.

The elimination method revolves around adding or subtracting multiples of equations from each other in order to eliminate variables. Pick a variable to eliminate and add or subtract suitable multiples of one equation to the other two to give a zero coefficient for that variable. This will leave you two equations in two variables. Pick another variable to eliminate and repeat the process. This will give you one equation in one variable which you can solve. Substitute this into one of the equations from the preceding step to find the second variable, and substitute both into one of the original equations to find the value of the first variable.

These techniques are the same ones used to solve equations with 2 variables. They can be extended indefinitely to systems of arbitrarily many variables, but there's no new principles.

Answer 5

you have 4 equations in 3 variables, so the two between the equations is redundant (between the others scaled) or incorrect. None of them seem redundant, so which you will get distinctive ideas counting on which 3 equations you employ. choosing the 1st 3 to artwork on, subtract the 1st 2 to get one equation in 2 variables, and subtract the 2d and 0.33 to get yet another equation in 2 variables. Take those 2 new equations and remedy them the way you may routinely do, then plug those numbers back in to get the 0.33 variable. yet back, the 4 equations as a team has no ideas, you will desire to %. 3 out of the 4. .

Answer 6

You need 3 equations then use any method you want. you can also use matrices