Comments on Two variable equation with only a few integer solutions

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Re: solving the two variable quadratic equation

x y + 3 x + 5 y = 62

Add 3*5 = 15 to both sides of the equation.

 

x y + 3 x + 5 y + 15 = 62 + 15 = 77

 

Factor both sides of the equation.

 

(x + 5) (y + 3) = 77 = 7 * 11

Then (x+5) can be      7, 11,   -7,  -11,   1, 77, -1, -77

and (y+3)  would be   11,  7, -11,  -7,   77,  1, -77,  -1

 

giving the 8 solutions

x =   2,  6,   -12,  -16,   -4,   72,   -6,   -82

y =   8,  4,   -14,  -10,   74,   -2,   -80,   -4

 

posted by Kermit1941 on February 24, 2015 at 11:28 AM | link to this | reply

I am stumped.

posted by FormerStudentIntern on February 23, 2015 at 11:34 AM | link to this | reply

Image result for confused emoticon

posted by Kabu on February 23, 2015 at 11:08 AM | link to this | reply