let use h= hotdogs price and c=chips price
we know that
4h +4c= 17
5h+3c=17.75
t use the elimination method we will multiply the first equation by 5 and the second one by (-4)
20h +20c=85
-20h -12c= -71
8c=14, we will divide by 8 both side and c=1.75, so a bag of potato chips cost $ 1.75
now we will substitute the c in the first equation
4h+7=17 therefore 4h=17-7, 4h=10, h=2.50
a bag of potato chips is 1.75
a hot dog costs 2.50