Answer:
[tex]x=3, y = 49\\x=0.5, y = -3.5\\x=-0.67, y = -2.31[/tex]
Step-by-step explanation:
[tex]y=6x^2-5\\y=17x-\frac{6}{x}[/tex]
Let's substitute the first equation into the second one.
[tex]6x^2-5=17x-\frac{6}{x}[/tex]
[tex]6x^3-17x^2-5x+6=0[/tex] - Multiply by [tex]x[/tex] and bring all the terms to one side.
I'll use my graphical calculator to solve this but you could factor:
[tex]x=3\\x=0.5\\x=-0.67[/tex] (All rounded to 2 decimal places)
Now we can substitute these [tex]x[/tex] values into an equation for [tex]y[/tex].
[tex]y=6x^2 - 5[/tex]
[tex]x=3, y = 49\\x=0.5, y = -3.5\\x=-0.67, y = -2.31[/tex]
