SOLUTION: Solve for X and Y : 8/x + 6/y = 6 and 1/x + 1/y = 1/6

Algebra ->  Equations -> SOLUTION: Solve for X and Y : 8/x + 6/y = 6 and 1/x + 1/y = 1/6      Log On


   

Question 842617: Solve for X and Y :
8/x + 6/y = 6 and 1/x + 1/y = 1/6
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
8/x + 6/y = 6 and 1/x + 1/y = 1/6
8/x + 6/y = 6 and 1/x + 1/y = 1/6
multiply the second equation by 36
36( 1/x + 1/y = 1/6 ) = 36/x + 36/y = 6
Since 8/x + 6/y = 6
8/x + 6/y = 36/x + 36/y
add -8/x -6/y to each side
0 = 28/x + 30/y
add -30/y to each side
-30%2Fy+=+28%2Fx
do cross products
28y = -30x
divide by 28
y = %28-30%2F28%29%2Ax
substitute %28-30%2F28%29%2Ax for y in 1/x + 1/y = 1/6
1%2Fx+%2B+1%2F%28%28-30%2F28%29%2Ax%29+=+1%2F6
1%2Fx+-+1%2F%28%2830%2F28%29%2Ax%29+=+1%2F6
1%2Fx+-+28%2F%2830%2Ax%29+=+1%2F6
%2830%2F30%29%2A%281%2Fx%29+-+28%2F%2830%2Ax%29+=+1%2F6
%2830%2F%2830%2Ax%29%29+-+28%2F%2830%2Ax%29+=+1%2F6
%282%2F%2830%2Ax%29%29++=+1%2F6
do cross products
30x=12
divide each side by 30
x = 12/30 = 2/5
We previously determined that y = %28-30%2F28%29%2Ax,
so substituting 2/5 for x we have
y = %28-30%2F28%29%2A%282%2F5%29
y = %28-60%2F140%29 = -3%2F7
summarizing x = 2/5 , y = -3/7