Question

(7) 99x + 101y = 499; 101x + 99y = 501​

Answer 1

Answer:

.99x + Ioly=499.... (i)

lolx +99y=50l.....(2)

Add(I) and (2)

2oox+2ooy=1000

divide by 200

x+y=5. ------........(3)

Subtract (2) from ( I)

- 2x+2y=-2

-x+y = -1........(4)

Solve (3) and (4) ->

x=3,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)