Question

solve and write the value of x and y. 99x + 101y = 499 ; 101x + 99y =501


​

Answer 1

99x + 101y = 499

+101x + 99y = 501

----–----------------------------------

200x + 200y = 1000

(200x + 200y = 1000)/200

x + y = 5 ..........1

99x + 101y=499 is subtracted from

101x + 99y = 501

= 2x - 2y = 2

=(2x - 2y = 2)/2

= x - y = 1. ....... 2

x + y = 5

x - y = 1

------------------

2x = 6

x = 3

x + y = 5

3 + y = 5

y = 5 - 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)