Question

Solve the following simultaneous equation.

99x + 101y = 499; 101x + 99y = 501

Answer 1

Adding equation (i) and (ii) we get,

99x + 101y = 499     ...(i)
101x + 99y = 501     ...(ii)
200x + 200y = 1000

x + y = `1000/200`       ...[Dividing both sides by 200]

∴ x + y = 5       ...(iii)

Subtracting equation (ii) from (i) we get,

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

–x + y = –1

x – y = 1      ...(iv)

 x + y = 5   ...(iii)
 x – y = 1    ...(iv)
2x = 6

∴ x = `6/2`

∴ x = 3

Put x = 3 in the equation no. (iii)

x + y = 5

3 + y = 5

∴ y = 5 – 3

∴ y = 2

x = 3, y = 2