To check which ordered pairs are solutions to the equation y=x²-x+3, we can substitute each of the x and y values into the equation and see if they make it a true statement.
For example,
For option A (-8,-5):
Substituting x=-8 and y=-5 in the equation, we get (-5) = (-8)²-(-8)+3, which simplifies to -5 = 77. This is false.
For option B (-4,-3):
Substituting x=-4 and y=-3 in the equation, we get (-3) = (-4)²-(-4)+3, which simplifies to -3 = 23. This is also false.
For option C (-2,4):
Substituting x=-2 and y=4 in the equation, we get 4 = (-2)²-(-2)+3, which simplifies to 4 = 9. This is true.
For option D (2,2):
Substituting x=2 and y=2 in the equation, we get 2 = 2²-2+3, which simplifies to 2 = 3. This is false.
For option E (4,-5):
Substituting x=4 and y=-5 in the equation, we get (-5) = 4²-4+3, which simplifies to -5 = 11. This is false.
Therefore, the only ordered pair that is a solution to the equation y=x²-x+3 is C. (-2,4).