How do I solve simultaneous equations with 3 unknowns with only 2 equations?

Question

x + y + z = 10
x*y*z = 10

EDIT: All these variables have at most 2 decimal place.

Answer 1

From iteration approach :
X = 1.08
Y = 7.72
Z = 1.20
U'll never completely finish the equation, unless you add more boundary condition.

Answer 2

You indicate us that the solution is : (a = 6, b = - 6, c = 1) If you want this solution to be correct, I think there is a little mistake in the equation (3). You must have : 9a + 3b + c = 54 - 18 + 1 = 37 instead of 36 (1) : a + b + c = 1 (2) : 4a + 2b + c = 13 (3) : 9a + 3b + c = 37 Do the calculation : (2) - (1), and get equation (4) (4) : 4a + 2b + c - a - b - c = 13 - 1 (4) : 3a + b = 12 (4) : b = 12 - 3a According the equation (3) (3) : c = 37 - 9a - 3b Replace "b" and "c" by them values into the equation (1) and get equation (5) : (5) : a + [b] + [c] = 1 (5) : a + [12 - 3a] + [37 - 9a - 3b] = 1 (5) : a + 12 - 3a + 37 - 9a - 3b = 1 (5) : - 11a - 3b = 1 - 12 - 37 (5) : - 11a - 3b = - 48 (5) : 11a + 3b = 48 From equation (4) : 3a + b = 12, multiply by 3 and get equation (6) : (6) : 9a + 3b = 36 Now, calculate (5) - (6) and get equation (7) : (7) : 11a + 3b - 9a - 3b = 48 - 36 (7) : 2a = 12 (7) : a = 6 According (4) : b = 12 - 3a b = 12 - 3(6) b = 12 - 18 b = - 6 According (1) : a + b + c = 1 c = 1 - a - b c = 1 - (6) - (- 6) c = 1 - 6 + 6 c = 1 Finaly, you obtain : a = 6, b = - 6, c = 1

Answer 3

It's not possible to solve for 3 unknowns with only 2 equations. There must be one equation per unknown. The best you can do is to get a value for one of them in terms of the other two.

Answer 4

You can't, unless you have some other information, for example, that all the variables are integers, or something.

In this case there's no obvious solution.
.

Answer 5

x + y + z = 10
x = 10 - y -z

x*y*z = 10
x = 10 / y*z

10 - y -z = 10 / y*z
y*z ( 10 - y -z ) = 10

Answer 6

If that's all you're given, there is a large set of answers.