Question

Simultaneous equation 99x+101=499:101x+99=501

Answer 1

Step-by-step explanation:

Let us use a trick to solve it quickly

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

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

subtract i from ii

2x - 2y = 2 or x - y =1 or x = 1 + y ....... ............... iii

add i and ii

200x + 200y = 1000 or x + y = 5 ...................................................................... iv

Now from iii and iv , we get 1 + y + y = 5 or 2y = 4 or y = 2 ...... v

again from iii and v , we get x = 1 + 2 = 3

Hence x = 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)