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Solve the following Two variable Linear equation 1/(2A)+1/(3B)=2, 1/(3A)+1/(2B)=13/6
CBSE | Class 10 | Exercise 3.3 | Maths | Pair of Linear Equations In Two Variables | RD Sharma
Solve the following Two variable Linear equation 1/(2A)+1/(3B)=2, 1/(3A)+1/(2B)=13/6

Let 1/A=u and 1/B=v,

So the given equations becomes,

u/2+v/3=2 ………………(i)

u/3+v/2=13/6 ……………(ii)

From (i), we get

u/2+v/3=2

⇒ 3u+2v=12

⇒ u=(12-2v)/3 ………….(iii)

Using (iii) in (ii)

[(12-2v)/3]/3+v/2=13/6

⇒ (12-2v)/9+v/2=13/6

⇒ 24-4v+9v=(13/6)A18 [after taking LCM]

⇒ 24+5v=39

⇒ 5v=15

⇒ v=3

Substituting v in (iii)

u=(12-2(3))/3

⇒ u=2

Thus, A=1/u ⇒ A=\frac{1}{2} and

B=1/v⇒B=1/3

The solution for the given pair of equations is A=\frac{1}{2} and B=1/3 respectively.

i

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