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June 10th, 2018, 12:27 AM   #1
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System of equations

Here is the system:
xy-Ax-Bx=0
xy-y-15x=0
The task is to find A and B. Is it possible?
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June 10th, 2018, 02:06 AM   #2
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Did you type the first equation correctly? It currently has x as a factor of every term.
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June 10th, 2018, 09:16 PM   #3
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Sorry, my typing mistake.
First equation is
xy-Ay-Bx=0

Last edited by skipjack; June 11th, 2018 at 06:36 AM.
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June 10th, 2018, 09:25 PM   #4
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Subtracting the second from the first gives -(A-1)y - (B-15)x = 0 and you can solve x for y or y for x in terms of A and B, or A and B for each other in terms of x and y, depending on what's variable and what's constant. But there's no unique solution without additional constraints. You can see that the xy term is a red herring here, right?

Last edited by skipjack; June 11th, 2018 at 06:43 AM.
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June 11th, 2018, 06:47 AM   #5
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If the equations have to hold for any values of x and y, it follows that A = 1 and B = 15.
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