Question

99x+101y=499; 101x +99y=501​

Answer 1

Step-by-step explanation:

99x + 101y=499............1

101x + 99y=501............2

digits are interchanged

(so add eqn)

200x + 200y = 1000

divide by 200

x + y = 5............3

(now substract)

-2x - 2y = -2

divide by 2

-x -y= 1

x - y = 1.........4

x+y=5.......3

x-y=1........4

______

add eqn 3 and 4

2x = 6

x= 6/2

x=3

substitute the value of x in 4 eqn

x-y=1

3-y=1

-y= 1-3

-y=-2

y=2

(3,2) is the solution of the given equation

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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)