Just make up 9 numbers, positive or negative 
at random, and use them as coefficients for 
x, y and z.

I made up these 9 numbers, completely at random

2,-5,3,-3,4,-2,1,5,-4

and put them as coefficients of x,y, and z, like this:
followed by an equal sign

 2x-5y+3z = 
-3x+4y-2z = 
  x+5y-4z = 

Then I substituted x=-2,y=3,and z=4 in each one, like this:

 2(-2)-5(3)+3(4) = -4-15+12 = -7
-3(-2)+4(3)-2(4) =  6+12-8  = 10
  (-2)+5(3)-4(4) = -2+15-16 = -3 

Then I put those results after the equal signs,
and got this system of 3 equations and 3 unknowns:

 2x-5y+3z = -7
-3x+4y-2z = 10
  x+5y-4z = -3

That system has the solution set (x,y,z) = (-2,3,4)

You can make up as many as you like.  This is
how teachers and people who write math books 
make up problems for students to solve. 

Edwin