Question

Which ordered pair is a solution to the following system of inequalities?y ≤ –x2 + 5xy > x2 – 4 (–1, –1) (0, 2) (2, 5) (4, 1)

Answer 1

Hello!

We have the following system:

`\begin{cases}y\le-x^2+5x{} \\ y>x^2-4{}\end{cases}`

Let's try to solve it by replacing each alternative:

(–1, –1) FALSE

`\begin{cases}-1\le-(-1)^2+5(-1){\rightarrow\boxed{-1\le-6}}\text{ FALSE} \\ -1>(-1)^2-4{{\rightarrow}\boxed{-1>-3}}\text{ TRUE}\end{cases}\text{ }`

(0, 2) FALSE

`\begin{cases}2\le-0^2+5(0){{\rightarrow}\boxed{2\le0}\text{FALSE}} \\ 2>0^2-4{{\rightarrow\boxed{2>-4}\text{ TRUE}}}\end{cases}`

(2, 5) TRUE

`\begin{cases}5\le-2^2+5(2){{\rightarrow}\boxed{5\le6}\text{ TRUE}} \\ 5>2^2-4{{\rightarrow\boxed{5>0}}}\text{ TRUE}\end{cases}`

(4, 1) FALSE

`\begin{cases}1\le-4^2+5({4)}{\rightarrow}\boxed{1\le4}\text{ TRUE} \\ 1>4^2-4{{\rightarrow}\boxed{1>12}\text{ FALSE}}\end{cases}`

Answer:

Alternative C. (2, 5).