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Question
Solve the following pairs of equations:
`x/(3) + y/(4)` = 11
`(5x)/(6) - y/(3)` = -7
Solution
`x/(3) + y/(4)` = 11
⇒ 4x + 3y = 132 ....(i)
`(5x)/(6) - y/(3)` = -7
⇒ 5x - 2y = -42 ....(ii)
Multiplying eqn. (i) by 2 and eqn. (ii) by 3, we get
8x + 6y = 264 ....(iii)
15x - 6y = -126 ....(iv)
Adding eqns. (iii) and (iv), we get
23x = 138
⇒ x = 6
Substituting the value of x in eqn. (i), we get
4(6) + 3y = 132
⇒ 24 + 3y = 132
⇒ 3y = 108
⇒ y = 36
Thus, the solution set is (6,36).
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