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! .
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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