.
First appearance of the system
10x + 10y = 20 (1)
2x + 14y = 13 (2)
Multiply equation (2) by 5 (both sides). Keep equation (1) as is.
Second appearance of the system
10x + 10y = 20 (1')
10x + 70y = 65 (2')
Now subtract equation (1') from equation (2'). The terms "10x" will cancel each other (ELIMINATION !), and you will get
60y = 45,
y = = of the dollar = $0.75.
Next substitute y = 0.75 into equation (1') to get
10x = 20 - 10*0.75 = 12.50,
x = 1.25.
ANSWER. The price for each coffee is $1.25; for each doughnut $0.75.