Question

Solve the following simultaneous equations:
103a + 51b = 617
97a + 49b = 583

Answer 1

The given equations are 
103a + 51b = 617     ....(i)
97a + 49b = 583      ....(ii)
Subtracting eqn. (ii) from (i). we get
6a + 2b = 34
⇒ 3a + b = 17      ....[Dividing throughtout by 2] ....(iii)
200a + 100b = 1200
⇒ 2a + b = 12    ...[Dividing throughtout by 100]  ....(iv)
Subtracting eqn. (iv) from eqn. (iii), we get
a = 5
Substituting the value of an in eqn. (iii), we get
3(5) + b = 17
⇒ 15 + b = 17
⇒ b = 2
Thus, the solution set is (5,2).