Solve the following system of equations:4/x + 3y = 8; 6/x −4y = −

1.	Solve the following system of equations:4/x + 3y = 8; 6/x −4y = −5
Answer» Taking \(\frac{1}{x}\) = u Then the two equation becomes, 4u + 3y = 8…………(i) 6u – 4y = -5……….(ii) From (i), we get 4u = 8 – 3y ⇒ u = \(\frac{(8 − 3y)}{4}\) …….. (iii) Substituting u in (ii) [6\(\frac{(8 − 3y)}{4}\)] – 4y = -5 ⇒ [\(\frac{3(8−3y)}{2}\)] − 4y = −5 ⇒ 24 − 9y −8y = −5 x 2 [After taking LCM] ⇒ 24 – 17y = -10 ⇒ -17y =- 34 ⇒ y = 2 Putting y = 2 in (iii) we get, u = \(\frac{(8 − 3(2))}{4}\) ⇒ u = \(\frac{(8 − 6)}{4}\) ⇒ u = \(\frac{2}{4}\) = \(\frac{1}{2}\) ⇒ x = \(\frac{1}{u}\) = 2 ∴ x = 2 So, the solution of the pair of equations given is x=2 and y =2.

Solve the following system of equations:4/x + 3y = 8; 6/x −4y = −5

Answer»

Taking \(\frac{1}{x}\) = u

Then the two equation becomes,

4u + 3y = 8…………(i)

6u – 4y = -5……….(ii)

From (i), we get

4u = 8 – 3y

⇒ u = \(\frac{(8 − 3y)}{4}\) …….. (iii)

Substituting u in (ii)

[6\(\frac{(8 − 3y)}{4}\)] – 4y = -5

⇒ [\(\frac{3(8−3y)}{2}\)] − 4y = −5

⇒ 24 − 9y −8y = −5 x 2 [After taking LCM]

⇒ 24 – 17y = -10

⇒ -17y =- 34

⇒ y = 2

Putting y = 2 in (iii) we get,

u = \(\frac{(8 − 3(2))}{4}\)

⇒ u = \(\frac{(8 − 6)}{4}\)

⇒ u = \(\frac{2}{4}\) = \(\frac{1}{2}\)

⇒ x = \(\frac{1}{u}\) = 2

∴ x = 2

So, the solution of the pair of equations given is x=2 and y =2.