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Chapter 3: Q46. (page 135)

Solve each system of inequalities by graphing.

46. 2y+x鈮�4y鈮�x鈭�4.

Short Answer

Expert verified

The solution set of the given system of inequalities is shown in the below graph:

Step by step solution

01

– Sketch the solution of the inequality 2y+x≥4.

Solve the equation 2y+x鈮�4for y:

2y+x鈮�42y鈮�鈭�x+4y鈮�鈭�x2+42y鈮�鈭�x2+2

The equation of the inequality y鈮�-x2+2is y=-x2+2which is a line equation with slope m=-12,and the y-intercept is 0,2.

Graphical interpretation of the given inequality 2y+x鈮�4:

02

– Sketch the solution of the inequality y≥x-4 .

The equation of the inequality y鈮�x-4 is y=x-4 which is a line equation with slope m=1and the y-intercept is 0,-4.

Graphical interpretation of the given inequality y鈮�x-4:

03

– Now sketch the solution set of the both the inequalities in the coordinate plane.

The solution set is the region colored in purple.

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Most popular questions from this chapter

Solve each equation. Check your solution.

68.4r+3-7=10

0.05n+0.10(n+8)=2.15

0.4x+0.6=0.5x-1.2

PointsA,B,C, and Dlie in consecutive order on a line. If AC=43ABand BD=6BC, then what isABCD?

12(x+4)=34
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