Question 173478
1/(2X-4)- 2/(y+1)=0 and 1/(x-3)- 1/(y+4)=0
Solve using elimination:
:
{{{1/((2X-4))}}}- {{{2/((y+1))}}} = 0
Multiply equation by (2x-4)(y+1) to get rid of the denominators, results
(y+1) - 2(2x-4) = 0
y + 1 - 4x + 8 = 0
-4x + y + 9 = 0
-4x + y = -9
4x - y = 9; multiplied by -1
 and 
{{{1/((x-3))}}} - {{{1/((y+4))}}} = 0
Multiply by (x-3)(y+4), results:
(y + 4) - (x - 3) = 0
y + 4 - x + 3 = 0
-x + y + 7 = 0
-x + y = -7
:
Add the two equations
4x - y = 9
-x + y = -7; 
---------------adding eliminates y, find x
3x = 2
x = {{{2/3}}}
:
Use the last equation to find y:
-{{{2/3}}} + y = -7
y = -7 + {{{2/3}}}
y = -6{{{1/3}}} or {{{-19/3}}}
:
:
Check solutions in the 2nd original equation:
{{{1/(((2/3)-3))}}} - {{{1/(((-19/3)+4))}}} = 0
{{{1/(((2/3)-(9/3)))}}} - {{{1/(((-19/3)+(12/3)))}}} = 0
{{{1/((-7/3))}}} - {{{1/((-7/3))}}} = 0
{{{-3/7}}} + {{{3/7}}} = 0
:
I'll let you check it in the 1st original equation