Question

Convert the following equations into simultaneous equations and solve:

`sqrt("x"/"y") = 4, 1/"x" + 1/"y" = 1/"xy"`

Answer 1

`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.