Answer:
a. (4, –7) and (0, –3)
Step-by-step explanation:
Easiest is to check the answer choices.
The constant in the first equation is -3, so we know that (0, -3) is a point on that graph. The sum of those two values is -3, so that is also a point on the graph of the line.
The only two answer choices with (0, -3) as one point are the first and last. The other point in the last answer choice is not on the line (4+7 ≠ -3).
So, the only viable answer choice is the first one.
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To solve the system algebraically, you can substitute the expression for y in the first equation into the second equation:
x + (-x^2 +3x -3) = -3
-x^2 +4x = 0 . . . . . . . . . add 3
-x(x -4) = 0 . . . . . . . . . . factor
Solutions are x = 0, x = 4. (These are the values of x that make the factors 0.)
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Evaluating the second equation to find y is easiest:
y = -3 -x
For x=0, y = -3.
For x=4, y = -7.
The solutions are (4, -7) and (0, -3).
