Solve and graph the system of inequalities: `y lt= 3/2 x + 3 ` `-y lt 2x` Please show all steps and graph.

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flbyrne | (Level 3) Assistant Educator

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Solve the system of linear inequalities by graphing each inequality and overlapping them.

To graph the line for ` y<=3/2x+3 ` , find the y intercept by substituting x=0 in y=3/2 x +3:

`y=3`. Find the x intercept by substituting y=0:

`3/2x+3=0 `

`3/2x=-3`

`x=-2`

Graph the line passing by (-2,0) and (0,3). Since the inequality is `<= ` , it is only true for the points below the line and includes the points on the line.

The line for the inequality -y<2x or y>-2x can be graphed by finding two points on the line. If x=0 then y=0, so (0,0) is one point. Find another point by substituting another number for x. Let's have x=1, then y=-2, then the second point is (1,-2). Graph y>-2x, since the inequality is > then it is true only for values above this line.

Combine both inequalities and shade the intersecting area (purple):

 

 

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