can we solve for x,y,z ?

Question

3x+2y+z=50

I have the following information.

x>=1
y>=1
z>=1

any of x,y,z could be >=10


can we solve for x,y,z ?

please advice some steps to follow.

thank you

Answer 1

As stated, you need three definitive equations (or variable values, any mix) in order to resolve a 3-variable equation down to a single point solution.

So there is an infinite number of points that satisfy the equation. Note that even with more restrictive values ranges for the three variables (perhaps x>=15, y>=2) you still have infinite values possible (with the above, z does not have to equal 1: x could be 15.2 and y could be 2 and so z would equal 0.4...).

schlouey is right about listing the information one CAN glean from the problem. Since it is the only material one can work out, the desired answer likely includes it along with the idea that there are still infinite solutions regardless of how the constraints constrain them.

Answer 2

No. What you can do is imagine the 3-D graph of the equation 3x+2y+z=50 and the inequalities x>=1, y>=1, and z>=1. The entire space within those bounds consists of solutions. There is not any ONE solution: there are infiniately many solutions.

Here are a few of them:
(2, 2, 40)
(10, 5, 10)
(3, 20, 1)

I hope this helps!

Answer 3

I don't believe you can solve this problem for one solution.

When you have three variables you typically need 3 equations or at least more specific information than what is listed here.

If it is any help, the most I can get from this is that

z<= 45
y<=23
z<=47/3

Answer 4

No, you can't solve it, you need to have three equations to solve it (the number of the variables).

Answer 5

3 unknowns...1 equation...infinite solutions