Question

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

Answer 1

99x+101y=499 -------(1)
101x+99y=501 -----------(2)
subtract (2)-(1)
(101-99) x+(99-101) y=501-499
2x-2y=2
x-y=1
x=y+1 now put x=y+1 in (1)
99(y+1)+101y =499
99y+99+101y=499
200y=400
y=2 now x=y+1=3
so , answer is x=3 and y=1

Answer 2

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)