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A system with two equations and three variable is known as a parametric equation and can be simplified, generally, to one equation with two variables.
You always need a number of equations equal to or greater than the number of variables you have to find any of the variables.
If you have more varibles than equations you can eliminate a number of variables equal to the number of equations minus one.
Edit: While this is correct, you can fudge an answer using a pseudoinverse. This minimizes one of the values, and then you can approximate the other two. Suppose you have:
3x + 2y + 4z = 0
x + 8y + 7z = 3
You can call this A*b = y, where
A = [3,2,4;1,8,7]
b = [x;y;z]
y= [0;3]
Then you can say
b=ay, where
a=A'(A*A')^(-1)
' indicated the transpose, and ^-1 indicates the inverse.
More explanation can be found at http://neurotheory.columbia.edu/~ken/math-notes/sabes.pdf
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Is it possible to find three unknowns with two equations if the two equations are equal?
No i believe that with three unknowns you must have three equal equations. Hope this helps! -dancinggirl25
What are the three types of possible solutions to a system of equations?
If the equations are linear, they may have no common solutions, one common solutions, or infinitely many solutions. Graphically, in the simplest case you have two straight lines; these can be parallel, intersect in a same point, or actually be the same line. If the equations are non-linear, they may have any amount of solutions. For example, two different intersecting ellipses may intersect in up to four points.
Do equations with different slopes and different y-intercepts have a solution?
TWO linear equations with different slopes intersect in one point, regardlessof their y-intercepts. That point is the solution of the pair.However, this does not mean that three (or more) equations in two variables, even if they meet the above conditions, have a solution.
What is a method used to solve systems of equations in which the solution is the point where the lines intersect?
there are three methods: combination, substitution and decomposition.
When solving a system of equations what does 4 equals 4 mean?
three things: 1) that the value of 4 is equal to the value of 4. 2) you did not obtain any revealing information. 3) your strategy for solving that system of equations was not good.
