Question

First clear the system of fractions, then solve by substitution
x/2-y/3=5/6
x/5-y/4=1/10

Answer 1

x/2-y/3=5/6
(x)/(2)-(y)/(3)=(5)/(6)

(x)/(2)=(y)/(3)+(5)/(6)

x=(2y+5)/(3)
-----------------------
x/5-y/4=1/10
(2y+5)/(3)/5-y/4=1/10

((2y+5)/(3))/(5)-(y)/(4)=(1)/(10)

(2y+5)/(15)-(y)/(4)=(1)/(10)

(2y+5)/(15)*(4)/(4)-(y)/(4)*(15)/(15)=(1)/(10)

((2y+5)(4))/(60)-(y(15))/(60)=(1)/(10)

((2y+5)(4)-(y(15)))/(60)=(1)/(10)

(-7y+20)/(60)=(1)/(10)

-7y+20=6

-7y=-14

y=2
---------------------------------------
x=(2y+5)/(3)
x=(2(2)+5)/(3)
x=(4+5)/(3)
x=9/3

x=3