[ [ equations in integers ]

Solve the equation $12 a+11 b=2002$ in natural numbers.

#
Since 11 and 2002 are divisible by 11, then $a=11 x$ and $12 x+b=182$. For each $x$ from 1 to 15, we get the answer ( $11 x, 182$ $-12 x$).

## Answer

(11, 170), (22, 158), (33, 146), (44, 134), (55, 122), (66, 110), (77, 98), (88, 86), (88, 74), (99, 62), (110, 50), $(121,38),(132,26),(143,14),(155,2)$.