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,
⇒ 9p – 4q = 8 …(i)
⇒ 13p + 7q = 101 …(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 7 and eq.(ii) by 4, so that variable q in both the equations have same coefficient.
Recalling equations (i) & (ii),
9p – 4q = 8 [×7
13p + 7q = 101 [×4
⇒ 115p = 460
⇒ p = 4
Substitute p = 4 in eq.(i)/eq.(ii), as per convenience of solving.
Thus, substituting in eq.(i), we get
9(4) – 4q = 8
⇒ 36 – 4q = 8
⇒ 4q = 36 – 8 = 28
⇒ q = 7
Thus, p = 4 and q = 7
As p = 1/x,
⇒ 4 = 1/x
⇒ x = 1/4
And q = 1/y
⇒ 7 = 1/y
⇒ y = 1/7
Hence, we have x = 1/4 and y = 1/7