Question

99x+101y=499
101x+99y=501
Find the value of x+y

Answer 1

Answer:

X+Y=5

Step-by-step explanation:

Let us take the first equation as 'a'

the second equation as 'b'

Multiply The equation 'a' with 101

It implies 9999X+10201Y=50399

Multiply The equation'b' with 99

It implies. 9999X+9801Y=49599

solving 'a' and 'b'

we get, Y=2

On substituting the value of Y in equation'a'

we get ,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)