Ariyonne claims that (3, 6) is the point of intersection of the lines y = 4x − 2 and y = + 5. Is she

IF the point  (3,6) solves BOTH of the equations, it is a common point to both lines.....substitute and see if it does!

incorrect. 

the point of intersection is ( 1.75,5 ) 

4x-2=5

4x=7

x=1.75 

this is how to find x .

to find y substitute the value of x in any equation. 

y = 4(1.75)-2 

y = 5 

Note......if we set the "y's" equal, then we have

4x - 2   = 5

Then.......the resulting x value for the solution of this equation is the x coordinate for the intersection point.......so.........add 2 to each side

4x  = 7     divide both sides by 4

x = 7/4      so........ (3, 6)  cannot possibly be the intersection point

And as  xvxvxv pointed out,  the intersection point is actually (7/4, 5)  or ( 1.75, 5)

Here's the graph of the intersection point to confirm this:   https://www.desmos.com/calculator/sl2lhr8m1w