Question

Solve
101 X + 99 Y = 499
99 X + 101Y = 501

Answer 1

Step-by-step explanation:

101 X + 99 Y = 499 ..... (i)

99 X + 101 Y = 501 .....(ii)

adding both the equation

200 X + 200 Y = 1000

taking 200 common we get

X + Y = 5 ..... (iii)

now subtracting eqn (i ) and (ii)

we get

2 X - 2 Y = -2

taking 2 common

X - Y = -1.... (iv)

now adding eqn (iii) and (iv)

we get 2X = 4 so X = 2

similarly putting it in eqn ( iii) we get value of Y = 3

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)