Question

hi please h3lp I have only 10 min to do this because it's due in 10 minutes and I've been trying to figure this out for a while

Answer 1

To graph the system

y ≤ 2x + 1

y < -x - 1

first, you have to graph the lines

y = 2x + 1

y = -x - 1

From the y-intercept and the slope, we know that the first line passes through the points:

(0, 1)

(0+1, 1+2) = (1, 3)

From the y-intercept and the slope, we know that the second line passes through the points:

(0, -1)

(0+1, -1-1) = (1, -2)

Next, we have to find if a point satisfies each equation or not, in order to know which region we have to shade. Taking for example the point (0, 0) and replacing it into the first inequality,

0 ≤ 2(0) + 1

0 ≤ 1

which is true, then we have to shade the region below the line y = 2x + 1

Replacing (0, 0) into the second inequality,

0 < -0 - 1

0 < -1

which is false, then we have to shade the region below the dotted line y = -x - 1

The final result is shown in the next picture.

This corresponds to graph X