# Solve for x and y: We have and where x≠0 and y≠0

Lets simplify these equations. Assuming 1/x = p and 1/y = q, we can rewrite them, 3p + 2q = 12 …(i) 2p + 3q = 13 …(ii)

To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.

Lets multiply eq.(i) by 2 and eq.(ii) by 3, so that variable p in both the equations have same coefficient.

Recalling equations (i) & (ii),

3p + 2q = 12 [×2

2p + 3q = 13 [×3 - 5q = - 15

q = 3

Substitute q = 3 in eq.(i)/eq.(ii), as per convenience of solving.

Thus, substituting in eq.(i), we get

3p + 2(3) = 12

3p + 6 = 12

3p = 12 – 6 = 6

p = 2

Thus, p = 2 and q = 3

As p = 1/x,

2 = 1/x

x = 1/2

And q = 1/y

3 = 1/y

y = 1/3

Hence, we have x = 1/2 and y = 1/3

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