Question

solve the following simultaneous equation and find value of x+y and 5x+5y
99x+101y=499
101x+99y=501​

Answer 1

Answer:

x+y = 5 and 5x+5y = 25

99x+101y=499---------------------(i)

101x+99y=501----------------------(ii)

On adding equation (i) and (ii), we get:-

99x+101y=499

+ 101x+99y=501

____________

200x +200y=1000

200(x+y)=1000

x+y=1000/200

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

On subtracting equation (i) and (ii), we get:-

99x+101y=499

101x+99y=501

-_________

-2x-2y=-2

-2(x-y)=-2

x-y=-2/-2

x-y=1---------------------(iv)

On adding equation (iii) and (iv), we get:-

x+y=5

x-y=1

+_____

2x=6

x=6/2

x=3

On substituting the value of x in equation (iii), we get:-

x+y=5

3+y=5

y=5-3

y=2

x=3,y=2

x+y=3+2=5

5x+5y=5(x+y)= 5(3+2)=5(5)=25