A kilogram of potatoes and 3 kilograms of tomatoes cost $3 while 2 kilogram of potatoes and 1 kilogram of tomatoes cost $7. How much does each cost?

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Let the cost of potatoes be P and that of tomatoes be T. We are given that 1 kg of potatoes and 3 kg of tomatoes cost $3:

=>  P + 3T = 3 ...(1)

And the cost of 2 kg of potatoes and 1 kg of tomatoes is $7

=> 2P + T = 7 ...(2)

We have to solve (1) and (2)

P  + 3T = 3

=> P = 3 – 3T

Substitute in (2)

2(3 – 3T) + T = 7

=> 6 – 6T + T = 7

=> -5T = 1

=> T = -1/5

P = 3 + 3/5

=> P = 18/5

But the cost of tomatoes cannot be negative, so we can say that we cannot get valid costs for the two from the information given.

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