Question

(Lesson 12.2) Graph the system of linear inequalities. Give two ordered pairs that are solutions andtwo that are not solutions. (2 points)9.sy 3x + 3w<-286I422 46 8-8 -6 -4 -20-2

Answer 1

Two ordered pairs (Solution) : (-4, -4) and (-3, -3)

Two ordered pairs (Not a solution) : (1, 1) and (2, 3)

EXPLANATION :

From the problem, we have :

`\begin{gathered} y\ge3x+3 \\ y<-2 \end{gathered}`

Note that the boundary line is dashed or broken if the inequality symbol is < or >.

Otherwise, the boundary line is a solid line.

Graph the first inequality :

Change the symbol to "="

`y=3x+3`

Solve for the x and y intercepts.

`\begin{gathered} \text{ when x = 0 :} \\ y=3(0)+3=3 \\ \\ \text{ when y = 0 :} \\ 0=3x+3 \\ -3x=3 \\ x=-(3)/(3)=-1 \end{gathered}`

Test the inequality at the origin (0, 0)

The region will pass through the origin if it satisfy the inequality.

`\begin{gathered} y\ge3x+3 \\ 0\ge3(0)+3 \\ 0\ge3 \\ \text{ False!} \end{gathered}`

Therefore, the region will NOT pass through the origin.

Plot the points (0, 3) and (-1, 0).

Connect it with a solid line.

The region will NOT pass the origin.

Graph the second inequality :

Change the symbol to "="

`y=-2`

Since y must be less than -2, the region is from y = -2 to the negative infinity.

Plot the point (0, -2) and draw a horizontal dashed line since the symbol is <.

That will be :

The solution to the inequality is the overlapping region.

Any point in the overlapping region is a solution.

Two ordered pairs solution are (-3, -3) and (-4, -4)

Two ordered pairs that are NOT a solution : (1, 1) and (2, 3)