Question 518930
x-y =9
x=y+9

1/x+1/y =5/12

substitute x 

{{{1/y+(1/(y+9))=5/12}}}

muktiply by y(y+9) the LCD

{{{((y+9)+y)/(y(y+9))=5/12}}}

{{{(2y+9)/(y(y+9))=5/12}}}

cross multiply

12(2y+9)=5(y(y+9))
24y+108=5y^2+45y
5y^2+21y-108=0

Find the roots of the equation by quadratic formula								
								
a=	5	,	b=	21	,	c=	-108	
								
b^2-4ac=	441	+	2160					
b^2-4ac=	2601		{{{	sqrt(	2601	)=	51	}}}
{{{y=(-b+-sqrt(b^2-4ac))/(2a)}}}								
{{{y1=(-b+sqrt(b^2-4ac))/(2a)}}}								
y1=(	-21	+	51	)/	10			
y1=	3							
y2=(	-21	-51	) /	10				
y2= 	-7.2							

 12 & 3 is one of the solution.

-7.2 & 1.8

m.ananth@hotmail.ca