Question

which answer can be used to find the solution to the system of equations?
\\(\bigcirc\\) \\(x = \frac{3}{x}\\)
\\(\bigcirc\\) \\(x = \frac{9}{x}\\)
\\(\bigcirc\\) \\(0 = \frac{3}{x} + x\\)
\\(\bigcirc\\) \\(0 = \frac{9}{x} + x\\)

Explanation:

Step1: Identify linear equation

The orange line is $y = x$ (slope=1, y-intercept=0).

Step2: Identify rational equation

The blue curve passes through $(-3, -3)$: substitute into $y=\frac{k}{x}$, get $-3=\frac{k}{-3}$, so $k=9$. Thus $y=\frac{9}{x}$.

Step3: Set equations equal

To find intersections, set $y=y$: $x=\frac{9}{x}$.

Answer:

$x=\frac{9}{x}$