Question

select the correct answer from the drop-down menu. consider the equations $y = \frac{1}{\sqrt{x}}$ and $y = x - 2$. the approximate solution of this system of equations is drop-down menu with options (-2.6, 0.6), (2.6, 0.6), (1.6, 2.6), (1.6, 0.6)

Explanation:

Step1: Set equations equal

$$x-2 = \frac{1}{\sqrt{x}}$$

Step2: Test valid x values

$x$ must be positive, eliminate $(-2.6, 0.6)$. Test $(2.6,0.6)$: $2.6-2=0.6$, $\frac{1}{\sqrt{2.6}} \approx \frac{1}{1.61} \approx 0.62$, matches closely.
Test $(1.6,0.6)$: $1.6-2=-0.4
eq 0.6$. Test $(1.6,2.6)$: $1.6-2=-0.4
eq 2.6$.

Answer:

(2.6, 0.6)