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Question
Solve the following simultaneous equations:
41x + 53y = 135
53x + 41y = 147
Solution
The given equations are
41x + 53y = 135 ....(i)
53x + 41y = 147 ....(ii)
Multiplying eqn. (i) by 53 and eqn. (ii) by 41, we get
2173x + 2809y = 7155 ....(iii)
2173x + 1681y = 6027 ....(iv)
Subtracting eqn. (iv) from eq. (iii), we get
1128y = 1128
⇒ y = 1
Substituting the value of y in eqn. (i), we get
41x + 53(1) = 135
⇒ 41x + 53 = 135
⇒ 41x = 135 - 53
⇒ 41x = 82
⇒ x = 2
Thus, the solution set is (2, 1).
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