Question

−10x − 5y ≥ 15

x + y ≤ −1

Select all the quadrants containing a solution to the above system of linear inequalities.

Select one or more:
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV

Please help, 30 points

Answer 1

B. Quadrent II I think

Answer 2

Actuallu it's Quadrant II, Quadrant III, Quadrant IV

Explanation:

Step 1

Recall that the solution of a system of linear inequalities is always a graph of the inequalities, so you will to need graph them.

Step 2

Rewrite each inequality in slope-intercept form.

−10x − 5y ≥ 15

−5y ≥ 10x + 15

y ≤ −2x − 3

x + y ≤ −1

y ≤ −x − 1

Step 3

Graph the lines representing each inequality.

The first inequality has a slope of −2 and a y-intercept of −3. Place a point at (0,−3), then move down by 2 and to the right by 1 and place a point at this location. Draw a line through the two points.

The second inequality has a slope of −1 and a y-intercept of −1. Place a point at (0,−1), then move down by 1 and to the right by 1 and place a point at this location. Draw a line through the two points.

Step 4

Shade the appropriate side of each line.

Both of the inequalities state y is less than or equal to some expression, so shade below each of the lines. The solution is the area of overlap between the two shadings.

Step 5

Observe your graph and match your solution to the correct answer choices.

Your graph of the linear inequalities shows solutions in Quadrants II, III, and IV. Select Quadrants II, III, and IV and move on to the next question.