Question

convert the following equation into simultaneous equations and solve : square root of x upon y is equal to 4 and one upon x plus one upon y is equal to one upon xy​

Answer 1

Answer: $x=\frac{16}{17}$ and $y=\frac{1}{17}$

Square root of x upon y is equal to 4 and one upon x plus one upon y is equal to one upon xy​.

Square root of x upon y is equal to 4

$\sqrt{\frac{x}{y} }=4$ --- 1

one upon x plus one upon y is equal to one upon xy.

$\frac{1}{x} +\frac{1}{y} =\frac{1}{xy}$ --- 2

Square both sides of 1

$\frac{x}{y} =16$

→ $x=16y$ --- 3

Multiply xy to both sides of 2

$x+y=1$

Put 3 into 2

$17y=1$

∴ $y=\frac{1}{17}$

Substitute into 3

∴ $x=\frac{16}{17}$