Question

if x + 2y = 9 and xy = 7, find the value of x + 4y.​

Answer 1

Answer:

x=2 or 7

y=1 or 7/2

x+4y=53

Answer 2

$xy = 7 \\ x = \frac{7}{y}$

Now put this value of x in x+2y=9

$\frac{7}{y } + 2y = 9 \\ \frac{7 + {2y}^{2} }{y} = 9 \\ 7 + {2y}^{2} = 9y \\ {2y}^{2} - 9y + 7 \\ {2y}^{2} - 7y - 2y + 7 \\ y(2y - 7) - 1(2y - 7) \\ (y - 1)(2y - 7) \\ \\ y = 1 \: or \: \frac{7}{2}$

Case 1. put y = 1 in x=7/y

x=7

Now put x= 7 and y= 1 in equation x+ 4y

= 7+4×1= 11

Case 2 put 7/2 in x= 7/y

x=2

Now put x= 2 and y= 7/2 in equation x+ 4y

=2 + 4× 7/2 = 2+14 = 16.

Value of x + 4y is 11 or 16