Answer
$(-\frac{1}{6},-6),(1,1)$
Work Step by Step
$6x-y=5$ Equation $(1)$
$xy=1$ Equation $(2)$
From Equation$(2)$
$y=\frac{1}{x}$ Equation$(3)$
Substitute $y=\frac{1}{x}$ in Equation$(1)$
$6x-y=5$
$6x-\frac{1}{x}=5$
$\frac{6x^{2}-1}{x}=5$
$6x^{2}-1 = 5x$
$6x^{2}- 5x-1 = 0$
By factoring,
$(6x+1)(x-1)=0$
$x = -\frac{1}{6}$ or $x=1$
Substitute $ x$ values in Equation $(3)$
Let $x = -\frac{1}{6}$
$y=\frac{1}{x}$
$y=\frac{1}{-\frac{1}{6}}$
$y = -6$
Let $x=1$
$y=\frac{1}{x}$
$y=\frac{1}{1}$
$y=1$
Solutions $(-\frac{1}{6},-6),(1,1)$ both satisfy both the equations.
So, the solutions are $(-\frac{1}{6},-6),(1,1)$
