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Question
Solve the following pairs of equations:
`(3)/(5) x - (2)/(3) y + 1` = 0
`(1)/(3) y + (2)/(5) x ` = 4
Solution
`(3)/(5) x - (2)/(3) y + 1` = 0
⇒ 9x - 10y + 15 = 0
⇒ 9x - 10y = -15 ....(i)
`(1)/(3)y + (2)/(5)x` = 4
⇒ 5y + 6x = 60
⇒ 6x + 5y = 60 ....(ii)
Multiplying eqn. (ii) by 2, we get
12x + 10y = 120 ....(iii)
Adding eqns. (i) and (iii), we get
21x = 105
⇒ x = 5
Substituting the value of x in eqn. (ii), we get
6(5) + 5y = 60
⇒ 30 + 5y = 60
⇒ 5y = 30
⇒ y = 6
Thus, the solution set is (5,6).
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