Solve for x and y:
We have
and
where y≠0
Lets simplify these equations. Assuming 1/y = z, we can rewrite them,
⇒ 2x – 3z = 9 …(i)
⇒ 3x + 7z = 2 …(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 3 and eq.(ii) by 2, so that variable x in both the equations have same coefficient.
Recalling equations (i) & (ii),
2x – 3z = 9 [×3
3x + 7z = 2 [×2
⇒ - 23z = 23
⇒ z = - 1
Substitute z = - 1 in eq.(i)/eq.(ii), as per convenience of solving.
Thus, substituting in eq.(i), we get
2x – 3( - 1) = 9
⇒ 2x + 3 = 9
⇒ 2x = 6
⇒ x = 3
Thus, z = - 1 and x = 3
As z = 1/y,
⇒ - 1 = 1/y
⇒ y = - 1
Hence, we have x = 3 and y = - 1