(1/5)x +(3/10)y = 7/50
(2/5)x +(1/2)y = 1/5
let's get rid of those fractions
multiply the top equation by 50
10x +15y = 7
(2/5)x +(1/2)y = 1/5
multiply the bottom equation by 10
10x +15y = 7
4x +5y = 2
let's eliminate the x
multiply the top equation by 2
20x +30y = 14
multiply the bottom equation by -5
20x +30y = 14
-20x -25y = -10
add the equations together
0x +5y = 24
5y = 24
y = 24/5
now go back to our two equations
10x +15y = 7
4x +5y = 2
multiply the bottom equation by -3
10x +15y = 7
-12x -15y = -6
add the equations together
-2x +0y = 1
-2x = 1
x = -1/2
Answer: x = -1/2, y = 24/5