Question

2/x+6/y=13;3/x-4/y=12

Answer 1

1/x=a : 1/y=b. 2a+6y=13. 3a-4b=12. solve it by substitution method answer of b=0.57. a=4.79. 4.79=x. 0.57=y I THINK IT IS USE FULL.

Answer 2

The answer is given below :

The given equations are

2/x + 6/y = 13 .....(i)

3/x - 4/y = 12 .....(ii)

Let us consider 1/x = p and 1/y = q.

Then, (i) and (ii) become

2p + 6q = 13 .....(iii)

3p - 4q = 12 .....(iv)

Now, we multiply (iii) by 3 and (iv) by 2. We get

2p + 6q = 13 .....(iii) × 3

3p - 4q = 12 .....(iv) × 2

⇒

6p + 18q = 39

6p - 8q = 24

On subtraction, we get

(6p + 18q) - (6p - 8q) = 39 - 24

⇒ 6p + 18q - 6p + 8q = 15

⇒ 26q = 15

⇒ q = 15/26

Now, putting q = 15/26 in (iii), we get

2p + (6 × 15/26) = 13

⇒ 2p + 90/26 = 13

⇒ 2p = 13 - 90/26

⇒ 2p = [(13 × 26) - 90]/26

⇒ 2p = (338 - 90)/26

⇒ 2p = 248/26

⇒ p = 248/52

⇒ p = 62/13

We considered p = 1/x and q = 1/y.

When p = 62/13

1/x = 62/13

⇒ x = 13/62

When q = 15/26

1/y = 15/26

⇒ y = 26/15

So, the required solution is

x = 13/62 and y = 26/15

VERIFICATION :

Putting x = 13/62 and y = 26/15 in L.H.S. of (i), we get

L.H.S. = 2/(13/62) + 6/(26/15)

= 124/13 + 45/13

= (124 + 45)/13

= 169/13

= 13 = R.H.S.

Again, putting x = 13/62 and y = 26/15 in L H.S of (ii), we get

L.H.S. = 3/(13/62) - 4/(26/15)

= 186/13 - 30/13

= (186 - 30)/13

= 156/13

= 12 = R.H.S.

Thus, the obtained values of x and y are verified.

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