Question

Solve the following simultaneous equations:
65x - 33y = 97
33x - 65y = 1

Answer 1

The given equations are
65x - 33y = 97    ....(i)
33x - 65y = 1     ....(ii)
Multiplying eqn. (i) by 33 and eqn. (ii) by 65, we get
2145x - 1089y = 3201   ....(iii)
2145x - 4225y = 65      ....(iv)
Subtracting eqn. (iv) from eq. (iii), we get
3136y = 3136
⇒ y = 1
Substituting the value of y in eqn. (ii), we get
33x - 65(1) = 1
⇒ 33x - 65 = 1
⇒ 33x = 1 + 65
⇒ 33x = 66
⇒ x = 2
Thus, the solution set is (2, 1).