Question

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

Answer 1

Step-by-step explanation:

adding both the equations we get

200x+200y=501+499

200(x+y)=1000

x+y=500 ----(1)

Similarly,

subtracting both the equations we get

2x-2y=501-499

2(x-y)=2

x-y=1 ----(2)

Adding both equations we get

(x+y)+(x-y)=500+1

x+y+x-y=501

2x=501

x=501/2

subtracting both equations we get

(x+y)-(x-y)=500-1

x+y-x+y=499

2y=499

y=499/2

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)