Question

Prove if the test point (2,-3) is a solution to the system:4x+3y > -6x-3y < -9

Answer 1

If the point (2,-3), then it must satisfy both inequalities.

Let's replace it with the first one

$\begin{gathered} 4x+3y>-6 \\ 4\cdot2+3\cdot(-3)>-6 \\ 8-9>-6 \\ -1>-6 \end{gathered}$

As you can observe, the test point satisfies the first inequality.

Let's evaluate the second one

$\begin{gathered} x-3y<-9 \\ 2-3(-3)<-9 \\ 2+9<-9 \\ 11<-9 \end{gathered}$

The test point doesn't satisfy the second inequality.

Hence, the test point is not a solution to the given system because it doesn't satisfy both inequalities.