Question

solve 99x + 101y = 499 and 101x + 99y = 501 find the value of x and y

Answer 1

99x + 101y= 499 .......1
101x + 99y = 501......2
By subtracting 1 and 2
101x + 99y = 501
-99x - 101y =-499
______________
2x - 2y = 2
2 (x-y) = 2
x-y =1_____3
By adding 1 &2
101x+99y=501
99x+101y=499
_________________
200x+200y = 1000
200(x+y)=1000
x+y = 5______4
By adding 3 and 4
x-y=1
x+y=5
_______
2x=6
x=3

x-y=1
3-y=1
-y= -2
y=2

Answer 2

Given:    $99x + 101y = 499$

              $101x + 99y = 501$

if we subtract both the equations, we get

             $-2x + 2y = -2$

              ∴ $x - y = 1$ ...............(1)

If we add both the given equations,

                  $200x + 200y = 1000$

                 $x + y = 5$ ...............(2)

Now adding (1) and (2),

                            $2x = 6$

                         $x = 3$

subtracting (1) and (2)

                  $2y = 4$

                   $y = 2$

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