Question

Find the system of inequalities which represents the shaded region on the coordinate plane.

Answer 1

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 please make as brainlelist