Question

Identify the graph and describe the solution set of this system of inequalities. y < –3x – 2 y > –3x + 8

Answer 1

y < -3x - 2

y = -3x - 2

for x = 0 → y = -3(0) - 2 = 0 - 2 = -2 → (0, -2)

for x = -2 → y = -3(-2) - 2 = 6 - 2 = 4 → (-2, 4)

y > -3x + 8

y = -3x + 8

for x = 0 → y = -3(0) + 8 = 0 + 8 = 8 → (0, 8)

for x = 2 → y = -3(2) + 8 = -6 + 8 = 2 → (2, 2)

Answer 2

Answer:

The system of inequalities  y < –3x – 2 y > –3x + 8 doesn't have any solution because their regions are non intersecting.

explanation:

Graphical representation

It is the representation of equations or inequalities to have the better understanding of equation . Also it help to know the maxima and minima of equation.

Here given equations are y < –3x – 2 , y > –3x + 8

$\begin{aligned}&y < -3 x-2 \\&y=-3 x-2\end{aligned}$

For $x=0 \Rightarrow y=-3(0)-2=0-2=-2 \Rightarrow(0,-2)$

For $x=-2 \Rightarrow y=-3(-2)-2=6-2=4 \Rightarrow(-2,4)$

$\begin{aligned}&y > -3 x+8 \\&y=-3 x+8\end{aligned}$

For $x=0 \Rightarrow y=-3(0)+8=0+8=8 \rightarrow(0,8)$

For $x=2 \Rightarrow y=-3(2)+8=-6+8=2 \rightarrow(2,2)$

Therefore by analyses of graph we can say  that the system of inequalities  y < –3x – 2 ,  y > –3x + 8 doesn't have any solution because their regions are non intersecting.

Learn  more about the Graphical representation here-

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