SOLUTION: The variable x varies jointly with y and z use the given vales to write an equation relating x,y and z. x=2 when y=3 and z=-4 then find y when x=8 and z=1

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Question 1074024: The variable x varies jointly with y and z use the given vales to write an
equation relating x,y and z. x=2 when y=3 and z=-4 then find y when x=8 and
z=1
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The variable x varies jointly with y and z use the given vales to write an equation relating x,y and z. x=2 when y=3 and z=-4, then find y when x=8 and z =1

For all such problems, start with this:

Varying           "directly" or product of "jointlys" or 1 if none 
quantity  = k * ----------------------------------------------------------
                inversely variable or product of "inverselys" or 1 if none

In this problem the varying quantity is x.
there are no "directly"s or "inverselys", so we have
the product of the jointlys on top and 1 on the bottom:

x=k%2A%28yz%2F1%29

x=k%2Ayz

>>...x = 2 when y = 3 and z = -4...<<

Substitute these values and solve for k:

x=k%2Ayz

%282%29=k%2A%283%29%28-4%29

2=k%2A%28-12%29

2%2F-12=k

-1%2F6=k

Next substitute -1/6 for k in

x=k%2Ayz

x=expr%28-1%2F6%29%2Ayz

That is the complete equation of variation,
which can be used to find any one of the three
variables when two of them are given

>>...find y when x=8 and z=1 <<

Now we substitute those values into

x=expr%28-1%2F6%29%2Ayz

and solve for y.

I'll let you do that.  If you have trouble, you
can tell me in the thank-you note form below,
and I'll get back to you by email.  No charge, 
as I do this for fun.  :)

Edwin