Question

1/7x+1/6y=3 ,1/2x-1/3y=5​

Answer 1

1/7x + 1/6y = 3 -------(1)

1/2x - 1/3y = 5 -------(2)

multiply equation 1 by 42 and equation 2 by 12. we get,

6x + 7y = 126 -------(3)

6x - 4y = 60 -------(4)

subtracting equation 4 from equation 3. we get,

11y = 66

therefore y = 6

putting value of y in equation 4

6x - 4×6 = 60

6x = 84

therefore x = 14

answer: x = 14 and y = 6

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

1/7x + 1/6y = 3 …………...(a)

1/2x - 1/3y = 5 …………...(b)

Now,

Multiply (b) by 1/2 we get,

1/4x - 1/6y = 5/2 ………....(c)

Now,

Add (a) and (c) we get,

1/7x + 1/4x = 3 + 5/2

(4 + 7)/28x = (6 + 5)/2

11/28x = 11/2

1/28x = 1/2

28x = 2

x = 2/28

x = 1/14

Now,

Substituting value of x in (a),

1/7x + 1/6y = 3

1/7(1/14) + 1/6y = 3

1/(1/2) + 1/6y = 3

1 × 2/1 + 1/6y = 3

2 + 1/6y = 3

1/6y = 3 - 2

1/6y = 1

6y = 1

y = 1/6

Therefore,

x = 1/14 & y = 1/6