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