Simultaneous equations?

Question

1/x + 2/y = 1/12 and 3/x + 1/y = 1/6

find x and y.

Answer 1

Let

1/x = u

1/y = v

u + 2v = 1/12

3u + v = 1/6

3u + 6v = 3/12

3u + v = 2/12

-----------------------

5v = 1/12

v = 1/60

u + 2/60 = 5/60

u = 3/60 = 1/20

x = 1/u = 20

y = 1/v = 60

Answer 2

1/x+2/y=1/12 (a)

3/x+1/y=1/6(b)

1/x+2/y=1/12 <=>(y+2x)/(xy)=1/12 <=>12(y+2x)=xy (1)

3/x+2/y=1/6 <=>(3y+2x)/(xy)=1/6 <=>6(3y+2x)=xy (2)

(1) & (2) ==>3y+2x=2(y+2x) <=>y=2x

Replace y in (a) by 2x ==>x, y

Answer 3

1/x + 2/y = 1/12

Multiply by 12xy, we get:

12y + 24x = xy--> (1)

and 3/x + 1/y = 1/6

Multiply by 6xy, we get:

18y + 6x = xy--> (2)

(2)*4 - (1) gives:

60y = 3xy => 3x = 60 => x =20 Substitute in (2), we get:

18y + 120 = 20y

2y = 120 => y = 60

Ans: X= 20 and Y = 60

AJM

Answer 4

assume 1/x=a and 1/y=b

then the equatuons becomes

a+2b=1/12------(1)

3a+b=1/6-------(2) consider as equation 1& 2

then

equtn  (1)*3-(2)

3a+6b=3/12

3a+b=1/6

--------------

0+5b=1/4-1/6

----------------------

5b=1/12

b=5/12

substituting in eqution (1)

we get

a+2*5/12=1/12

a=1/12-1/6

a=-1/12

so finally a=1/x so x= -12

and b=1/y so y=12/5