Question

​​3x/2 - 5y/3 = -2 and x/3 + y/2 = 13/6

Answer 1

3x/2-5y/3=-2
or, (9x-10y)/6=-2
or, 9x-10y=-12
or, x=(10y-12)/9
x/3+y/2=13/6
or, {(10y-12)/9}/3+y/2=13/6
or, (10y-12)/27+y/2=13/6
or, (20y-24+27y)/54=13/6
or, 47y-24=13/6×54
or, 47y=(13×9)+24
or, y=(117+24)/47
or, y=141/47
or, y=3
∴, x=(10y-12)/9
      =(10×3-12)/9
      =(30-12)/9
      =18/9
      =2
∴, x=2, y=3

Answer 2

$\frac{3x}{2} - \frac{5y}{3} = -2$
On taking LCM and simplification, we get
9x - 10y = -12    ....(1)

$\frac{x}{3} + \frac{y}{2} = <span>\frac{13}{6}</span><span>$
On simplification, 

2x + 3y = 13    ......... (2)

Multiply the (1) by 3 and the equation (2) by 10
27x - 30y = -36
20x + 30y = 130
Adding both equations, we get
47x = 94
x = 2

Substitute x = 2 in equation (2) 
2(2) + 3y = 13
3y = 9
y = 3