Question

Couldn’t figure this out, please help

Answer 1

(A)

Step-by-step explanation:

This system of equations will no solution if they have the same slope and only differ in the y-intercept values. So let's rewrite the two equations into their slope-intercept forms:

$y = \frac{3}{h-2}x + 5$

$y = \frac{8}{h}x + \frac{5}{h}$

For them to have no solution, their slopes must equal each other:

$\dfrac{3}{h-2} = \dfrac{8}{h} \Rightarrow 3h=8h-16$

or

$h = \dfrac{16}{5}$

Putting this value into our system of equations, we get

$y = \frac{5}{2}x + 5$

$y = \frac{5}{2}x + \frac{25}{16}$

This is a system of equations consisting of two parallel lines and as such, do not intersect and so, no solution.