Question

solve the following pairs of linear equation by reducing them to a pair of linear equation( 1/2x)+(1/3y)=2​

Answer 1

1/2x + 1/3y = 2

1/3x + 1/2y = 13/6

Let 1/x = p and 1/y = q, then the equations changes as below:

p/2 + q/3 = 2

⇒ 3p + 2q -12 = 0 ... (i)

p/3 + q/2 = 13/6

⇒ 2p + 3q -13 = 0 ... (ii)

By cross-multiplication method, we get

p/-26-(-36) = q/-24-(-39) = 1/9-4

p/10 = q/15 = 1/5

p/10 = 1/5 and q/15 = 1/5

p = 2 and q = 3

1/x = 2 and 1/y = 3

Hence, x = 1/2 and y = 1/3

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