Question

Is (1,3) a solution to the system of inequalities below?y>2x+1y<-3xWhy or why not ?

Answer 1

In order for (1,3) to be a solution of the inequalities system it must fultill all of them, for that reason we know that x=1 and y=3 and replace in both of the equations

`\begin{gathered} y>2x+1 \\ 3>2\cdot1+1 \\ 3>3 \end{gathered}`
`\begin{gathered} y<-3x \\ 3<-3\cdot1 \\ 3<-3 \end{gathered}`

(1,3) is not a solution to the system because it doesn´t fulfill any of the equations; it creates 2 false statements because 3 is not greater that 3, but its the same and also 3 is not less than -3 but the opposite.