Instructions: Determine which of the points given are in the solution area for the system of inequalities

Question

asked Feb 23, 2023 202k views

1 Answer

Rambo Ramon · Answer 1 · 2023-03-01T22:43:17+0000

Given the following inequalitites:

$\begin{gathered} y\leq(1)/(2)x+2 \\ y\ge-2 \\ x\leq-3 \end{gathered}$

We are going to evaluate each point:

A= (-10 , 1)

B= (-3, 7 )

C= ( 5 , 1)

D= (-3 , -5)

The point A:

$\begin{gathered} 1\leqslant(1)/(2)(-10)+2=1\leqslant-5+2=1\leqslant-3 \\ \end{gathered}$

As -3 is not greater or equal to 1 the point A does not work.

Point B:

$7\leqslant(1)/(2)(-3)+2=7\leqslant-(3)/(2)+2=7\leqslant(1)/(2)$

1/2 is not greater or equal to seven, the point B does not work.

Point C.

$1\leqslant(1)/(2)(5)+2=1\leqslant(5)/(2)+2=1\leqslant(9)/(2)$

9/2 is greater than 1, now we have to evaluate the other inequalities in the same point.

$\begin{gathered} 1\ge-2 \\ and \\ 1\leq-3 \end{gathered}$

As -3 isn't greater than 1, the point c does not work.

The point D.

$-3\leqslant(1)/(2)(-5)+2=-3\leqslant-(1)/(2)$

The first one is true, -1/2 is greater than -3.

$-5\ge-2$

The second one is false, the point D does not work.

Point E (0 , 0).

$0\leqslant(1)/(2)(0)+2=0\leq2$

The first is true.

Second one:

$0\ge-2$

The second one is true.

Third one.

$0\leq-3$

The point E does not work, because -3 is not greater or equal to -3.

Answer: no point is a solution of the system.