Question

Solve the following simultaneous equations:
13a - 11b = 70
11a - 13b = 74

Answer 1

The given equation are
13a - 11b = 70     ....(i)
11a - 13b = 74    ....(ii)
Multiplying eqn. (i) by 13 and eqn. (ii) by 11, we get
169a - 143b = 910   ....(iii)
121a - 143b = 814   ....(iv)
Subtracting eqn. (iv) from eq. (iii), we get
48a = 96
⇒ a = 2
Subtracting the value of a in eqn. (i), we get
13(2) - 11b = 70
⇒ 26 - 11b = 70
⇒ -11b = 70 - 26
⇒ -11b = 44
⇒ b = -4
Thus, the solution set is (2, - 4).