Final answer:
The linear equations b. 2x - 8 = 0 and d. 4x + 4 = 0 each have one solution. The quadratic equations a. x^2 - 9 = 0 and c. 3x^2 - 27 = 0 each have two solutions as they are perfect square trinomials.
Step-by-step explanation:
Among the given equations, b. 2x - 8 = 0 and d. 4x + 4 = 0 have one solution because they are linear equations with the form ax + b = 0. If an equation is linear and not a trivial equation (e.g., 0x + 0 = 0, which would have infinite solutions), it will always have exactly one solution.
Equations a. x^2 - 9 = 0 and c. 3x^2 - 27 = 0 are quadratic equations because they can be written in the form ax² + bx + c = 0, with the 'b' term being zero. These equations may have one, two, or no real solutions depending on the discriminant (b² - 4ac). In these particular cases, both a. and c. have two real solutions, as they are perfect square trinomials that factor into (x - 3)(x + 3) = 0 and (x - 3√3)(x + 3√3) = 0, respectively.