Question

Solve101x+99y=501; 99x+101y=499

Answer 1

Answer:

y= 2, x= 3

Step-by-step explanation:

Subtract one equation from the other we get as,

2x- 2y = 2

or, x - y = 1.

multiply the above equation by 101,

therefore, 101x - 101y = 101

subtract the first equation and this equation, we get 200y = 400 or y = 2.

substituting y = 2 in the equation we get,

101x = 303 or x = 3.

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)