SOLUTION: 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

Question 1038576: 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
Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
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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
~~~~~~~~~~~~~~~~~~~~~~~~~~

-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 Geometric interpretation of the linear system of two equations in two unknowns in this site.

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