Math, asked by Debdas1583, 10 months ago

X+y+xy=44 how many ordered pairs (x,y) satisfy the given condition

Answers

Answered by amitnrw

Step-by-step explanation:

x + y + xy = 44

=> x + y(1 + x) = 44

=> y(1 + x) = 44 - x

=> y = (44 - x)/(1 + x)

=> y = (45 - 1 - x)/(1 + x)

=> y = (45 - (1+ x) ) /(1 + x)

=> y = 45/(1 + x) - 1

y would be integer for 1 + x Being factor of 45

1+ x can be 1 , 3 , 5 , 9 , 15 , 45

x = 0 , x = 2 , x = 4 , x = 8 , x = 14 , x = 44

y = 44 y = 14 , y = 8 , y = 4 , y = 2 , y = 0

Ordered Pairs :

(0, 44) , ( 2, 14) , (4 , 8) , (8 , 4) , (14 , 2) , (44 , 0)

Considering - Ve values also

1+ x can be -1 , -3 , -5 , -9 , -15 , -45

x can be -2 , - 4 , - 6 , - 10 , - 16 , - 46

y -46 , -16 , -10 , - 6 , -4 , - 2

Ordered pairs

(-2 , - 46) , (-4 , -16) , (-6 , -10) , (-10 , 6) , (16 , -4) , (-46 , -2)

Total Ordered Pairs = 12

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