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Question
Convert the following equations into simultaneous equations and solve:
`sqrt("x"/"y") = 4, 1/"x" + 1/"y" = 1/"xy"`
Solution
`sqrt("x"/"y") = 4`
Squaring on both sides, we get
`"x"/"y"` = 16
∴ x = 16y ..........(i)
`1/"x" + 1/"y" = 1/"xy"`
Multiplying both sides by xy, we get
y + x = 1
i.e., x + y = 1 …(ii)
Substituting x = 16y in equation (ii), we get
16y + y = 1
∴ 17y = 1
∴ y = `1/17`
Substituting y = `1/17` in equation (i), we get
x = 16y = `16/17`
∴ (x, y) = `(16/17, 1/17)` is the solution of the given equations.
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