Question 1038576
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in the system of equations below, u and v are constants. If the system has more than one solution, what is the value of u/v?

   -2x + uy = v 
    x-2y = 3
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-2x + uy = v,      (1)
  x - 2y = 3.      (2)

Multiply equation (2) by -2. You will get an equivalent system

-2x + uy =  v,     (1')
-2x + 4y = -6.     (2')

The system (1'), (2') has more than one solution if and only if 

  u = 4  and  v = -6.

Why it is so?  -  Read the lesson <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Geom-interpret-of-the-lin-system-of-two-eqns-with-two-unknowns.lesson>Geometric interpretation of the linear system of two equations in two unknowns</A> in this site.
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