For this case we have the following system of equations:
[tex]y = x ^ 2-6x + 12\\y = 2x-4[/tex]
Equating the equations:
[tex]x ^ 2-6x + 12 = 2x-4\\x ^ 2-6x-2x + 12 + 4 = 0\\x ^ 2-8x + 16 = 0[/tex]
We look for two numbers that when multiplied, get 16, and when added together, get -8.
These numbers are -4 and -4.
[tex](x-4) (x-4) = 0\\(x-4) ^ 2 = 0[/tex]
So, the solution is[tex]x = 4[/tex]
We look for the value of y:
[tex]y = 2x-4\\y = 2 (4) -4\\y = 8-4\\y = 4[/tex]
Finally, the solution is:[tex](4,4)[/tex]
ANswer:
[tex](4,4)[/tex]
