Solve the system of equations:
y= X-3
y= x2 - 5x+ 6

(3, 0)

Step-by-step explanation:

As the first step in solving this system, substitute x - 3 for y in y= x^2 - 5x+ 6.  This temporarily eliminates y and gives us the equation in x  x - 3 = x^2 - 5x + 6, which simplifies to x^2 - 6x + 9, whose roots are {3, 3}.  When x = 3,  y = 0.  Thus, the solution is (3, 0).

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4