Question

Which ordered pair is a solution to the following system of inequalities?

y < –x2 + x

y > x2 – 4

(0, –1)
(1, 1)
(2, –3)
(3, –6)

Answer 1

Answer: (0,-1)

Step-by-step explanation:

Let's start with the first inequality, $y < -x^{2}+x$. To check which points satisfy this inequality, we can substitute the x- and y-coordinates and see if they satisfy the inequality.

• A) $-1 < -0^{2}+0 \longrightarrow -1 < 0 \longrightarrow \text{ True}$
• B) $1 < -1^{2}+1 \longrightarrow 1 < 0 \longrightarrow \text{ False}$
• C) $-3 < -2^{2}+2 \longrightarrow -3 < -2 \longrightarrow \text{ True}$
• D) $-6 < -3^{2}+3 \longrightarrow -6 < -6 \longrightarrow \text{ False}$

Once again, we can repeat this for the second inequality (but this time, we only need to check the points that satisfy the first inequality).

• A) $-1 > 0^{2}-4 \longrightarrow -1 > -4 \longrightarrow \text{ True}$
• C) $-3 > 2^{2}-4 \longrightarrow -3 > 0 \longrightarrow \text{ False}$

Therefore, the answer is (A) (0, -1).