Question

Which ordered pair is a solution to the system of inequalitiesy<|x| and y<-2x-1

Answer 1

Hello!

We have the following system:

`\begin{cases}y\le|x| \\ y<-2x-1\end{cases}`

To solve this exercise, we can try all alternatives and check which of them are true. Let's do it:

A) (3, 1) false

`\begin{cases}1\le|3|\text{ ok} \\ 1<-2\cdot3-1\rightarrow1<-6-1\rightarrow1<-7\text{ not ok}\end{cases}`

B) (2, -1) true

`\begin{cases}-1\le|2|\text{ ok} \\ -1<(-2\cdot-1)-1\rightarrow-1<2-1\rightarrow-1<1\text{ ok}\end{cases}`

C) (0, 4) false

`\begin{cases}4\le|0|\text{ not ok} \\ 4<-2\cdot0-1\rightarrow4<-1\text{ not ok}\end{cases}`

D) (-3, 1)