let

x = the caloric content of one pizza

y = the caloric content of one shake

One pan pizza and two shakes provide 3430 calories:

x + 2y = 3430

Two pan pizzas and one shake provide 2690 calories:

2x + y = 2690

by solving the system of equations:

x + 2y = 3430

2x + y = 2690

we find:

x = 650 calories

y = 1390 calories

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one pan pizza contains 650 calories.

one milk shake contains 1390 calories.