Question

solve for x and y x+2/x-2=y+8/y+4, 2x-5/4y-1=x-1/2y+1​

Answer 1

Answer:

x = -2 and y= -2

Step-by-step explanation:

Given first expression

$\frac{x + 2}{x - 2} = \frac{y + 8}{y + 4}$

(x+2)(y+4) = (x-2)(y+2) => xy +2y+4x+8 = xy-2y+2x-4

=>xy+2y+4x+8-xy+2y-2x+4=0

=>2x+4y+12=0 => x+2y= -6

second expression

$\frac{2x - 5}{4y - 1} = \frac{x - 1}{2y + 1}$

(2x-5)(2y+1) = (x-1)(4y-1) => 4xy-10y+2x-5= 4xy-4y-x+1

=> 4xy-10y+2x-5-4xy+4y+x-1=0

=>3x-6y-6=0 => x-2y = 2

by adding equation 1 and equation 2 we get

x+2y+x-2y =-6+2 => 2x = -4 =>x = -4/2 => x=-2

by substituting x in equation 1

x+2y = -6 => -2+ 2y = -6 => 2y =-6+2 =>2y = -4

=> y = -4/2 => y =-2