Question

99x+101y = 499 ; 101x+99y = 501 is

Answer 1

Answer:

$99x + 101y = 499........(1) \\ 101x + 99y = 501........(2) \\ (1) + (2) \\ 200x + 200y = 1000 \\ 200(x + y) = 1000 \\ x + y = 5............(3) \\ \\ (2) - (1) \\ 2x - 2y = 2 \\ 2(x - y) = 2 \\ x - y = 1............(4) \\ (3) + (4) \\ 2x = 6 \\ x = 3......in \: (3) \\ 3 + y = 5 \\ y = 2 \\ so \: x = 3 \: and \: y = 2 \\ = = = = = = = = = = =$

Answer 2

Answer:

99x + 101y = 499 .....(I)

101x + 99y = 501 .....(II)

Adding (I) and (II)

200x+200y=1000

⇒x+y=5 .....(III)

Subtracting (II) from (I)

99x−101x+101y−99y=499−501

⇒−2x+2y=−2

⇒−x+y=−1 .....(IV)

Adding (III) and (IV)

x+y=5−x+y=−1

⇒2y=4

⇒y=2

Putting the value of y = 2 in (III) we get

x+2=5⇒x=5−2=3

Thus, (x, y) = (3, 2)