Question

Which system of inequalities is represented by the graph?
http://curriculum.kcdistancelearning.com/courses/ALG1x-HS-A06/b/Exams/6Exam/6Exam_q26.bmp
A.) y > -2 and y > 2x + 1
B.)y > -2 and y < 2x + 1
>>>>>C.)y < -2 and y < 2x + 1
D.)y < -2 and y > 2x + 1
check this one too this time please explain
@evilmath
@texaschic101

Answer 1

Notice that there are two shaded bits which intersect to form a 'darker' shaded bit. I assume that's the region they want you to define.
Let's take it step by step.
1)Focus on orange part. The area shaded is above y = -2. so we say that corresponds to y > -2 (> for above)
2) What about the blue part? Well the line cutting off that part is y = 2x + 1. Notice how the blue shaded part is always below this line, not above. So this means The region corresponds to anything below the line, hence y < 2x + 1 (< for below line). You can check by substituting a point definitely in the region eg. (0,0) into the eqn:
y < 2x+1 ? --> 0 < 2(0) + 1 ?--> 0 < 1 TRUE so y < 2x + 1
Almost done. Since we are only interested in the intersection of the two regions, we say the region described is y > -2 AND y < 2x +1. (If interested in the union of the regions, we use the word OR)