Answer:
the answer is option D: (-2.2, 5.9) and (2.8, -3.0).
Explanation:
To solve the system of equations, we need to find the values of x and y that satisfy both f(x) = 2x^2 - 3x and g(x) = -3x^2 + 20, where f(x) = y and g(x) = y.
Setting the two expressions for y equal to each other, we have:
2x^2 - 3x = -3x^2 + 20
Bringing all the terms to one side, we get:
5x^2 - 3x - 20 = 0
We can solve for x using the quadratic formula:
x = [-(-3) ± √((-3)^2 - 4(5)(-20))] / 2(5)
Simplifying, we get:
x = [3 ± √289] / 10
x = [3 ± 17] / 10
x = 2 or -2/5
Now, we can substitute each value of x into either f(x) or g(x) to find the corresponding y-value.
For x = 2, we have:
f(2) = 2(2)^2 - 3(2) = 4 - 6 = -2
g(2) = -3(2)^2 + 20 = -12 + 20 = 8
Therefore, the solution for (x, y) is (2, -2) for this case.
For x = -2/5, we have:
f(-2/5) = 2(-2/5)^2 - 3(-2/5) = 8/25 + 6/5 = 14/25
g(-2/5) = -3(-2/5)^2 + 20 = -12/25 + 20 = 488/25
Therefore, the solution for (x, y) is (-2/5, 488/25) for this case.
Hence, the answer is option D: (-2.2, 5.9) and (2.8, -3.0).