Question

दिलेलं एकसामयिक समीकरण सोडवा: 99x + 101y = 499; 101x + 99y = 501

Answer 1

99x + 101y = 499------------(1)
101x + 99y = 501 ------------(2)

adding equation no. 1 and 2
99x + 101y = 499
+ 101x + 99y = 501
---------------------------
200x + 200y = 1000
: . dividing by 200
x + y = 5 ---------(3)

subtracting equation no.1 from 2
101x + 99y = 501
- 99x + 101y = 499
---------------------------
2x - 2y = 2
: . dividing by 2
x-y = 1 ----------(4)

adding equation no.3 and 4
x+ y= 5
+x- y = 1
------------
2x = 6
x = 6/2
x = 3

put x =3 in equation no. 3
x+ y =5
3+y = 5
y= 5-3
y =2

(x,y) = (3,2) is the soln of given problem

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)