# 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,

5p – 3q = 1 …(i)

9p + 4q = 30 …(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 4 and eq.(ii) by 3, so that variable q in both the equations have same coefficient.

Recalling equations (i) & (ii),

5p – 3q = 1 [×4

9p + 4q = 30 [×3

47p = 94

p = 2

Substitute p = 2 in eq.(i)/eq.(ii), as per convenience of solving.

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

5(2) – 3q = 1

10 – 3q = 1

3q = 10 – 1 = 9

q = 3

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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