Question

Solve 99 x + 101 y is equal to 499 and 101x + 99y is equal to 501

Answer 1

It is given that 99x+101y = 499
101x+99y = 501
Here we have to follow 2 cases
Addition n subtraction
So now we could add
99x+ 101y = 499
101x+ 99y = 501
When we add we will get
200x+ 200y = 1000
If we take 200 common , we will get
200(x+y)= 1000
x+y= 1000÷200
x+y=5.......equation(1)
Now to 2nd case..we need to subtract
99x-101y=499
101x-99y=501
On subtracting we'll get
-2x+2y= -2
-2(x-y) = -2
x-y = -2÷ -2
x-y = 1........ equation (2)
Now using elimination method solve
x+y = 5 (+)
x-y = 1
We'll get x=3 and y=2
Now substitute x and y and check whether these values are corrct

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)