What is the solution for the following pair of linear equations?
12x−1y=−1
1x+12y=8
(Where x≠0,y≠0)
x=16,y=14
We have
12x−1y=−1….(1)
1x+12y=8….(2)
From equation (1), 12x=−1+1y
⇒12x=(−y+1)y
⇒2x=y(−y+1)
⇒x=y(−2y+2)
Putting x=y(−2y+2) in equation (2),
(−2y+2)y+12y=8
⇒(−4y+4+1)2y=8
⇒−4y+4+1=16y
⇒20y=5
⇒y=14
Putting y=14 in equation (1),
⇒12x−4=−1
⇒12x=3
⇒x=16