Solving Linear Simultaneous Equations ?

(x + y)/(x - y) = 3
(x - 2)/(y - 9) = 10
Cross multiply:
x + y = 3(x - y)
x - 2 = 10(y - 9)
Distributive property:
x + y = 3x - 3y → -2x = -4y → x = 2y
x - 2 = 10y - 90 → 2y - 2 = 10y - 90 → -8y = -88 → y = 11

x = 2y = 2(11) = 22

To verify the answer:
(x + y)/(x - y) = (22 + 11)/(22 - 11) = 33/11 = 3
(x - 2)/(y - 9) = (22 - 2)/(11 - 9) = 20/2 = 10

(x + y)/(x - y) = 3 (solve by using substitution)
(x - 2)/(y - 9) = 10

(x + y)/(x - y) = 3
x + y = 3(x - y)
x + y = 3x - 3y
x - 3x = -y - 3y
-2x = -4y
x = -4y/-2
x = 2y

(x - y)/(y - 9) = 10
(2y - y)/(y - 9) = 10
y = 10(y - 9)
y = 10y - 90
y - 10y = -90
-9y = -90
y = -90/-9
y = 10

(x + y)/(x - y) = 3
x + 10 = 3(x - 10)
x + 10 = 3x - 30
x - 3x = -10 - 30
-2x = -40
x = -40/-2
x = 20

∴ x = 20 , y = 10

(x + y) / (x - y) = 3
x + y = 3x - 3y
2x - 4y = 0

(x - 2) / (y - 9) = 10
x - 2 = 10 y - 90
x - 10 y = - 88

- 2 x + 20 y = 176
2 x - 4 y = 0----------ADD

16 y = 176
y = 11

2x - 44 = 0
x = 22

x = 22 , y = 11

( x + y ) / ( x - y ) = 3 ------> (1)
( x - 2 ) / ( y - 9 ) = 10 ------> (2)

( x + y ) = 3 ( x - y )
x = 3x -3y -y
-2x = -4y (Divide by -2)
x = 2y ---------> Replace in (2)

( 2y - 2) / ( y - 9) = 10
2y - 2 = 10 y -90
-8 y = -88 (Divide by -8 )
y = 11

x = 2y = 2*11
x = 22

x+y = 3x-3y, 2x = 4y, x = 2y

x-2 = 10y-90, 2y-2 = 10y-90, 8y = 88

y= 11, x = 22.