At first glance this horrifying because of the fractions!
Luckily with equations you can always get rid of any fractions by multiplying each term by the LCM of the denominators.
#xx6 rarr " "x/2+(2y)/3=32" "rarr 3x+4y = 192#
#xx 36rarr" "x/4-(5y)/9=40" "rarr 9x -20y = 1440#
The equations look much better, now we can solve them:
#color(white)(..............)3x+4y = 192......................................A#
#color(white)(..............)9x-20y= 1440...................................B#
#A xx-3:" "color(blue)(-9x)-12y = -576......................C#
#color(white)(........................)color(blue)(9x)-20y= 1440.........................B#
#C+B:" "-32y =864#
#color(white)(................................)color(red)(y=-27)#
Substitute #-27 # for #y# in #A#
#" "3x+4(-27) = 192......................................A#
#" "3x-108 = 192#
#" "3x = 192+108#
#" "3x = 300#
#" "color(blue)(x = 100)#
Check the solutions in equation B
#" Is " 9(100)-20(-27)= 1440 ?#
#" "900+540= 1440#
#" Indeed! "1440 = 1440#
We can even check in the original equation for A;
#x/2+(2y)/3=32#
#100/2 +(2xx-27)/3#
#=50-18#
#=32" "larr# the answer is correct.
