Question

99x+101y=499; 101x+99y=501 Solve the simultaneous equation

Answer 1

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

adding equations (1) and (2),
=> (99 + 101)x + (101 + 99)y = 499 + 501
=> 200x + 200y = 1000
=> x + y = 5 , y = 5 - x put it in equation (1),

99x + 101(5 - x) = 499
=> 99x + 505 - 101x = 499
=> -2x = 499 - 505 = -6 .
=> -2x = -6
=> x = 3 , and y = 5 - x = 5 - 3 = 2

hence, x = 3 and y = 2

Answer 2

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

adding----( 1 ) & -----( 2 )

99x + 101y = 499
101x + 99y = 501
---------------------------
200x + 200y = 1000

x + y = 5-------------( 3 )

subtracting--------( 1 ) &-----( 2 )

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

x - y = 1----------( 4 )


from--------( 3 ) &------( 4 )

x + y = 5
x - y = 1
—————
2x = 6

x = 6/2 = 3 [ put in---( 3 )]

3 + y = 5

y = 5 - 3

y = 2 , x = 3