Question

Solve x and y.
99x+101y=499
101x+99y=501​

Answer 1

hey mate

here is your solution..

adding the equation

200x+200y=1000

200(x+y)=1000

x+y=5

subtracting the equation

2x-2y=2

2(x-y)=2

x-y=1

on solving the equation

2x=6

x=3

and thus, 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)