Which linear inequality is represented by the graph? y > 2x + 2 y ≥ One-halfx + 1 y > 2x + 1 y ≥ One-halfx + 2

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12th

Maths

Linear Programming

Graphical Solution of a Linear Inequation

If the system of inequaliti...

MATHS

If the system of inequalities y≥2x+1 and y>

2

1

x−1 is graphed in the xy-plane above, which quadrant contains no solutions to the system?

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December 26, 2019

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Rupashree Gøyaľ

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ANSWER

given, y≥2x+1 and

y>

2

1

x−1

first, draw the graph for equations y=2x+1 and y=

2

1

x−1

for y=2x+1

substitute y=0 we get, 2x+1=0⟹x=−0.5

substitute x=0 we get, y=1

therefore, y=2x+1 line passes through (0.5,0) and (0,1) as shown in fig.

Hence, y≥2x+1 includes the region above the line.

for y=

2

1

x−1

substitute y=0 we get,

2

1

x−1=0⟹x=2

substitute x=0 we get, y=−1

therefore, y=2x+1 line passes through (2,0) and (0,-1) as shown in fig.

Hence, y>

2

1

x−1 includes the region above the line.

the intersection region is the shaded region as shown in above figure which includes I, II and III quadrants.

Therefore, quadrant IV has no solution

solution