Question

1/3x + 1/5y =1/15 ;
1/2x + 1/3y=1/12
solve the question ​

Answer 1

Answer:

1/3x + 1/5y = 1/15;  1/2x + 1/3y = 1/12

1/3x + 1/5y = 1/15

Multiplying the equation by 15 on both the sides we get,

5/x + 3/y = 1

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

Multiplying the equation by 12 on both the sides we get,

6/x + 4/y = 1

Now,

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

∴ We get, 5a + 3b = 1 ......... eq. no. (1)

and 6a + 4b = 1 ........ eq. no. (2)

Multiplying (1) bt 4, we get

20a + 12b = 4 .........(3)

Multiplying (2) by 3, we get

18a + 12b = 3 ........(vi)

Subtracting  (4) from (3),

20a + 12b = 4

18a  + 12 b = 3

 -       -          -

2a =             1

∴ a = 1/2

Substituting a = 1/2  in equation (2)

∴ 6a + 4b = 1

∴ 6(1/2) + 4b = 1

∴ 3 + 4b = 1

∴ 4b = 1 – 3

∴ 4b = - 2

∴ b= - 2 /4

∴ b = -1/2

Substituting the values of a and b,

a = 1/2

∴ 1/x = 1/2

∴ x = 2

b = -1/2

∴ 1/y = -1/2

∴ y = -2

∴ x = 2  and y = - 2 is the solution of given simultaneous equations.

Step-by-step explanation:

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Answer 2

Answer:

1/3x + 1/5y =1/15

Take Lcm 15xy,

(5y+3x)/15xy = 1/15

5y+3x = (1/15)(15xy)

5y+3x = xy

(5y+3x)/xy = 0

(5y/xy)+(3x/xy)=0

5/x+3/y=0

Take 1/x as u and 1/y as v

5u+3v=0----------Equation 1

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

Take Lcm as 6xy,

(3y+2x)/6xy = 1/12

3y+2x = (1/12)(6xy)

3y+2x = xy/2

2(3y+2x) = xy

6y+4x = xy

(6y+4x)/xy=0

(6y/xy)+(4x/xy)=0

(6/x) + (4/y) = 0

Put 1/x as u and 1/y as v,

6u+4v=0

Take 2 common,

2(3u+2v) = 0

3u+2v = 0---------Equation 2

5u+3v=0----------Equation 1(multiply by 2)

3u+2v = 0---------Equation 2(multiply by 3)

We get,

10u+6v=0

9u+6v=0

Change signs,

10u+6v=0

-9u-6v= -0

We get,

u=0

As 5u+3v=0,

5(0)+3v=0

3v=0

v=0

Threfore x=0 and y=0.

I don't think this is the right answer.

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I am posting this coz i took almost 30 minutes to solve this .