Question

solve the given system of equations
99x+101y=499
101x+99y=501

Answer 1

99x+101y = 499---1 eqn
101x+99y= 501----2 eqn

add 1+2eqn

99x + 101y = 499
+101x + 99y = 501
_______________
200x+200 y= 1000
divide each term by 200

x + y = 5----------3

Subtract 1-2

99x + 101y= 499
- 101x+ 99y = 501
- - -
_______________
-2 x + 2y = -2
divide each term by 2

-x + y = -1----------4

add 3+4

x + y = 5
- x + y = -1
__________
2y= 4

y = 4 /2

y = 2

put y = 2 in eqn 3
x + y = 5
therefore
x+ (2) = 5
x = 5 - 2

x= 3




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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)