Answer:
18. (x, y) ∈ {(-2, -11), (0, -3)}
20. x < 3; x² -1 < y < x² -x +2
Step-by-step explanation:
18. Equate the values of y, then solve for x.
... 4x -3 = -x^2 +2x -3
... x^2 +2x = 0
... x(x +2) = 0
The values of x that make these factors zero are ...
... x = 0, x = -2
The corresponding values of y are ...
- 4·0 -3 = -3
- 4·(-2) -3) = -11
So, the solutions are (x, y) = (0, -3) or (-2, -11).
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20. This can be worked the same way to find a range of x that will make the system of equations true. The range of y must be computed based on that.
... x^2 -1 < y < x^2 -x +2
... x < 3 . . . . . . . . add -x^2 +x +1
The allowed range of y will vary with x, so the solution can be expressed as ...
... x < 3 and x^2 -1 < y < x^2 -x +2
