Answer:
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).
