# If 23x + 7y + 25z = 7200, how do I work out the values of x,y and z?

nick-teal | Certified Educator

Your teacher is probably asking you to find the roots of the function.

A normal 2d function has roots where the line crosses the x axis (points).

But since this is 3d we will need to find where the plane created by this equation passes through the xy plane, the yz plane, and the xz plane.  This will give us 3 different lines, I bet this is what your teacher is asking you to find.

In order to find where this equation passes through the xy plane, set z equal to zero and solve for one of the variables.

`23x + 7y + 25*0 = 7200`

`23x + 7y = 7200`

`y = (7200 - 23x)/7`

This is one of the 3 roots of the function, you would find the other two the same way, but by setting y or x equal to zero.

durbanville | Certified Educator

As there is only one equation and you have three unknown values, you will only be able to solve for x,y and z in terms of each other. If you have other information, you can then use that to develop your answer further.

If `23x +7y +25z = 7200`

then  `23x= 7200 - 7y - 25z`

`therefore x=(7200-7y-25z)/23`

and to repeat the process for y: `7y = 7200 - 23x - 25z`

`therefore y=(7200-23x-25z)/7`

and to repeat for z: `25z=7200 -23x -7y`

`therefore z=(7200-23x-7y)/25`

With more information you can then substitute into any other equation which relates to your information so that you can solve it.

`therefore x=(7200 - 7y-25z)/23` ; `y=(7200-23x-25z)/7`  ; `z=(7200-23x-7y)/25`

kspcr111 | Student

If 23x + 7y + 25z = 7200, how do I work out the values of x,y and z?

sol:-

As in the question there is only one Equation and three Unknowns (x,y and z). In order to get the exact values of the x,y and z we need three equations as there are three unknowns.

So in the above question, the Exact values of x,y,z cannot be determined but only the expressions as given by "durbanville " can be obtained.

For this equation

23x + 7y + 25z = 7200

The possible exact values of x,y and z are in infinite number of solutions.

Where x,y and Z belongs to Real Numbers