Choose the system of inequalities that matches the graph below.

Question

Choose the system of inequalities that matches the graph below.


coordinate plane with a dashed line through points (0, -1) and (1, 4). Another dashed line passes through points (0, 2) and (1, -1). There is yellow shading above the first dashed line and blue shading above the second dashed line. The shading turns green in the overlap
 
Choose one answer.
A. y>(line underneath) 5x - 1
y>(line underneath) -3x + 2
 

B. y<(line underneath) 5x - 1
y <(line underneath)-3x + 2
 

C. y > 5x - 1
y > -3x + 2
 

D. y < 5x - 1
y < -3x + 2

Answer 1

May -

 

It appears from your description that the overlapping area is above both of these lines, correct? 

And that both the lines are dashed. Neither is solid. 

 

So, immediately, we can eliminate choices A and B above, because they have greater than OR equal to (in A) and less than OR equal to (in B). We know that can't be the case because both lines are dashed. If they were solid that would indicate the "equals to" portion of the sign. 

 

So now we just have to decide between C and D. Since the shading is above both lines I like to say the shading is "uphill" and to me that indicates a "greater than sign" or choice C But you could test a few points in the overlapping area to make sure. 

 

the point (1,5) lies in this region. Does it satisfy both equations? 

 

5 > 5 (1) -1 √

5 >-3(1) +2 √

 

Does that make sense?