(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:
[tex]y = \frac{3}{h-2}x + 5[/tex]
[tex]y = \frac{8}{h}x + \frac{5}{h}[/tex]
For them to have no solution, their slopes must equal each other:
[tex]\dfrac{3}{h-2} = \dfrac{8}{h} \Rightarrow 3h=8h-16[/tex]
or
[tex]h = \dfrac{16}{5}[/tex]
Putting this value into our system of equations, we get
[tex]y = \frac{5}{2}x + 5[/tex]
[tex]y = \frac{5}{2}x + \frac{25}{16}[/tex]
This is a system of equations consisting of two parallel lines and as such, do not intersect and so, no solution.
