The correct option is
B x=14;y=17The equation 9x−4y=8 can be solved as:
9x−4y=8
⇒9y−4xxy=8
⇒9y−4x=8xy.........(1)
The equation 13x+7y=101 can be solved as:
13x+7y=101
⇒13y+7xxy=101
⇒13y+7x=101xy.........(2)
Multiply the equation 1 by 7 and equation 2 by 4. Then we get the equations:
63y−28x=56xy.........(3)
52y+28x=404xy.........(4)
Add equations 3 and 4 to eliminate x, because the coefficients of x are the opposite. So, we get
(63y+52y)+(−28x+28x)=56xy+404xy
i.e. 115y=460xy
i.e. 115=460x
i.e. x=115460=14
Substituting this value of x in the equation 1, we get
9y−4(14)=8(14)y⇒9y−1=2y⇒9y−2y=1⇒7y=1⇒y=17
Hence, the solution of the equations is x=14,y=17.