Which system of linear inequalities is represented by the graph?
O y2x - 2 and y = x + 1
O y< x-2 and y> x + 1
O y < x-2 and y? x + 1
O y> x-2 and y < x + 1

answer c.

y <= x - 2 and y >= x + 1

Step-by-step explanation:

You wrote the given answers wrong. Here are the right choices that are given as possible solutions:

O y >= x - 2 and y <= x + 1

O y < x - 2 and y > x + 1

O y <= x - 2 and y >= x + 1

O y > x - 2 and y < x + 1

The graph clearly shows two lines and the intended area is shaded and it is clearly including the lines.

Because the lines are included in the solution, by that alone, you can exclude two answers b and d.

Now you still need to decide between the in equalities in answer a and c. Both lines have a gradient of 1, so that does not help to distinguish...

The y intercept of the top line is at y= +1 and the shaded area is bigger then that

By now it is absolutely clear that answer c must be the right answer and you are done!

EXTRA

Although you have deduced beyond any doubt, that answer c must be the right answer, you still can check your findings 'to be sure' by looking and checking for the bottom line...

BE CAREFUL, ONLY DO THIS IF YOU HAVE ENOUGH TIME. Again, you already know the right answer, and this is "just to confirm", so what is the harm in that?

By double checking yourself, it will sort of "undermine" your appproach. Basically you are doing something which is strictly spoken not nessasary any more. So I urge you to basically step over the urge to check yourself, and stick to your answer.

However, if you can not resit the temptation of checking to see if you actually found the right answer, you could test the y intercept of the bottom line, which is at y= -2 and the shaded area is smalller then that

So again, it is now confirmed that answer c is indeed the right answer.

7

step-by-step explanation: