How to solve this example

if 20 lb of rice and 10 lb of potatoes cost 12.20$ and 30 lb of rice and 12 lb of potatoes cost 17.04$ how
much will 10 lb of rice and 50 lb of potatoes cost ?

let x= be the price per lb of rice
y = be the price per lb of potatoes
20x + 10y = 12.20
30x + 12y = 17.04
3(20x + 10y = 12.20) - 2(30x +12y = 17.04)
(60x + 30y = 36.60) - (60x + 24y = 34.08)
6y =2.52
y = .42 ,the price of per lb of potatoes
20x + 10(.42) = 12.20
20x + 4.2 =12.20
20x =12.20 - .2
x=.4, the price per lb of rice
so 10x + 50y
10(.4) + 50(.42)
4 + 21 = 25, the price of 10lb of rice and 50lb 0f potatoes

20r + 10p =12.20 → 60r + 30p = 36.60
30r + 12p = 17.04 → 60r + 24p = 34.08 Subtract

6p = 2.52 → p = 0.42 per pound of potatoes
20r + 10(0.42)p =12.20 → 20r + 4.20 =12.20 → 20r = 8.00 → r = 0.40 per pound of rice

Now solve for your final question