Question

Which ordered pair is included in the solution set to the following system?y < x2 + 3y > x2 – 2x + 8A. (–4, 2)B. (0, 6)C. (1, 12)D. (4, 18)

Answer 1

Answer:

The correct answer is the last option: (4, 18)

Explanation:

To know if an ordered pair is in the solution set of a system, the ordered pair must to verify all the inequalities in the system.

The system given is:

$\begin{cases}y<{x^2+3} \\ y>{x^2-2x+8}\end{cases}$

If we take the last option, the ordered pair (4, 18), and replace in both expressions x = 4 and y = 18, we see that the two expressions returns a true value:

$\begin{gathered} 18<4^2+3 \\ . \\ 18<16+3 \\ . \\ 18<19\text{ }True \end{gathered}$$\begin{gathered} 18>4^2-2\cdot4+8 \\ . \\ 18>16-8+8 \\ . \\ 18>16\text{ }True \end{gathered}$

Thus, the pair which is included in the solution set is the last one.