What is the value of
1/x-1/y, if 6/x-3/y=10 and 2/x-5/y=6
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6(1/x)-3(1/y)=10
Let 1/x=$ and 1/y=@
6$-3@=10—————- 1
Now
2(1/x)-5(1/y)=6
2$-5@=6—————— 2
Multiplying eq 1 by 1 and eq 2 by 3 we get
6$-3@=10————- 3
6$-15@=18———— 4
On subtracting 3 and 4 we get
12@=-8
@=-8/12
@=-2/3
We know that
1/y=@
1/y=-2/3
Now,
Substituting @=-2/3 on eq 1 we get
6$-3*-2/3=10
6$+2=10
6$=8
$=8/6=4/3
We also know that
$=1/x
4/3=1/x
So,
1/x-1/y =4/3-(-2/3)
=(4/3)+(2/3)
=6/3
=2
Hope this helps you
Let 1/x=$ and 1/y=@
6$-3@=10—————- 1
Now
2(1/x)-5(1/y)=6
2$-5@=6—————— 2
Multiplying eq 1 by 1 and eq 2 by 3 we get
6$-3@=10————- 3
6$-15@=18———— 4
On subtracting 3 and 4 we get
12@=-8
@=-8/12
@=-2/3
We know that
1/y=@
1/y=-2/3
Now,
Substituting @=-2/3 on eq 1 we get
6$-3*-2/3=10
6$+2=10
6$=8
$=8/6=4/3
We also know that
$=1/x
4/3=1/x
So,
1/x-1/y =4/3-(-2/3)
=(4/3)+(2/3)
=6/3
=2
Hope this helps you
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