Question

Which graph represents the system of linear inequalities given below

Answer 1

Answer and Step-by-step explanation:

First, graph these two lines as if they are regular equations, instead of inequalities (see attachment: the red line is $y = x - 3$ and the blue line is $y = -x + 2$).

Then, we need to determine which area to shade. For y ≤ x - 3, let's plug in a value like (0, 0): 0 ≤ 0 - 3  ⇒  0 ≤ -3; this is clearly NOT true because 0 is greater than -3, so we know that we cannot shade above the line y = x + 3. Instead, we shade below (see attachment 2: it's the red shaded part).

Now, for y > -x + 2. First, notice that since there is no equal part here, the line will be dotted. Now, let's plug in (0, 0) as well: 0 > -0 + 2  ⇒  0 > 2; again, this is clearly NOT true, so we know that we cannot shade in the area to the left of this line that includes the point (0, 0). Instead, we shade the area to the right (see attachment 2: it's the blue shaded).

Finally, look for the answer choice that matches the picture. The solution of this system is just the place where the shaded areas overlap.

Hope this helps!

Answer 2

Answer:

Region should be below the line:

y = x - 3

This line should be bold, have a positive slope and pass through (0,-3)

And above the line:

y = -x + 2

This line should be dotted, have a negative slope and pass though (0,2)

It's neither A nor B. Has to be one of the remaining options