Solve the system of equations

y=x-3

y=x^2-5x+6

x=3 (double root)

Step-by-step explanation:

We are told that y = x - 3.

Substituting x - 3 for y in the second equation yields:

x - 3 = x² - 5x + 6.

We need to rewrite this in the standard form of a quadratic equation:

Subtracting (x - 3) from both sides results in:

0 = x² - 5x + 6 - x + 3.

Combining like terms gives us:

0 = x² - 6x + 9,

which factors into (x - 3) (x - 3) = 0. Thus, there are two real, equal roots: x = 3 and x = 3.

Subbing 3 for x in the first equation gives us 3 - 3 = 0 = y ...

Thus, the solution of this system of equations is (3, 0).