Final answer:
The system of equations has one solution, found by equating the two equations, resulting in the quadratic equation x² - 6x + 9 = 0, which factors to (x - 3)(x - 3) = 0, leading to a single solution x = 3. Therefore, the correct answer is option a) 1.
Step-by-step explanation:
To determine how many solutions there are for the system of equations given, we can set the two equations equal to each other, since they both equal y:
y = x² - 5x + 3
y = x - 6
By setting them equal to each other:
x² - 5x + 3 = x - 6
Rearrange the equation by subtracting x and adding 6 to both sides:
x² - 6x + 9 = 0
This is a quadratic equation which can be factored as:
(x - 3)(x - 3) = 0
Therefore, x = 3 is the only solution for x, indicating that there is only one point where the two graphs intersect, hence there is one solution to the system of equations.
Correct answer: (a) 1