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On a piece of paper, graph this system of inequalities. Then determine whichregion contains the solution to the system.y<-3x+3y> 3x+ 2

On a piece of paper, graph this system of inequalities. Then determine whichregion-example-1
User Rohaq
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1 Answer

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The first step is to write the expressions as equations. We would substitute different values of x into each equation and find the corresponding y values. These values would be plotted on the graph and the lines would be solid because the points on the lines are inclusive. Thus, we have

For y = - x/3 + 3

if x = - 1, y = - - 1/3 + 3 = 1/3 + 3 = 10/3

if x = 0, y = - 0 * 3/3 + 3 = 0 + 3 = 3

If x = 1, y = - 1/3 + 3 = 8/3

For y = 3x + 2,

if x = - 1, y = 3(-1) + 2 = - 3 + 2 = - 1

If x = 0, y = 3(0) + 2 = 0 + 2 = 2

If x = 1, y = 3(1) + 2 = 3 + 2 = 5

We would plot these points on the graph as shown below

The red line represents y ≤ - x/3 + 3

Testing the point, x = 0, y = 0 on this inequality, it satisfies it. Hence, the area shaded red contains (0, 0)

The black line represents y ≥ 3x + 2

Testing the point, x = 0, y = 0 on this inequality, it does not satisfies it. Hence, the area shaded black does not contain (0, 0)

The region containing the shaded region is where the red and black regions overlap. Thus, the correct option is D

On a piece of paper, graph this system of inequalities. Then determine whichregion-example-1
User Yris
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