Solve for x and y:\(\frac{9}x-\frac{4}y=8\),\(\frac{13}x+\frac{7}y=101

1.	Solve for x and y:\(\frac{9}x-\frac{4}y=8\),\(\frac{13}x+\frac{7}y=101 \)
Answer» The given equations are: \(\frac{9}x-\frac{4}y=8\)........(i) \(\frac{13}x+\frac{7}y=101 \).......(ii) Putting 1/x = u and 1/y = v, we get: 9u - 4v = 8 …….(iii) 13u + 7v = 101 ……(iv) On multiplying (iii) by 7 and (iv) by 4, we get: 63u - 28v = 56 ……..(v) 52u + 28v = 404 ……..(vi) On adding (v) from (vi), we get: 115u = 460 ⇒ u = 4 ⇒ 1/x = 4 ⇒ x = 1/4 On substituting x = 1 4 in (i), we get: \(\frac{9}{\frac{1}{4}}\) - 4/y = 8 ⇒ 36 - 4/y = 8 ⇒ 4/y = (36 – 8) = 28 y = 4/28 = 1/7 Hence, the required solution is x = 1/4 and y = 1/7.

Solve for x and y:\(\frac{9}x-\frac{4}y=8\),\(\frac{13}x+\frac{7}y=101 \)

Answer»

The given equations are:

\(\frac{9}x-\frac{4}y=8\)........(i)

\(\frac{13}x+\frac{7}y=101 \).......(ii)

Putting 1/x = u and 1/y = v, we get:

9u - 4v = 8 …….(iii)

13u + 7v = 101 ……(iv)

On multiplying (iii) by 7 and (iv) by 4, we get:

63u - 28v = 56 ……..(v)

52u + 28v = 404 ……..(vi)

On adding (v) from (vi), we get:

115u = 460 ⇒ u = 4

⇒ 1/x = 4 ⇒ x = 1/4

On substituting x = 1 4 in (i), we get:

\(\frac{9}{\frac{1}{4}}\) - 4/y = 8

⇒ 36 - 4/y = 8

⇒ 4/y = (36 – 8) = 28

y = 4/28 = 1/7

Hence, the required solution is x = 1/4 and y = 1/7.