270,527 views
41 votes
41 votes
Which graph represents the solution to this system of inequalities? y ≤ -2x y > 3x − 4

Which graph represents the solution to this system of inequalities? y ≤ -2x y &gt-example-1
Which graph represents the solution to this system of inequalities? y ≤ -2x y &gt-example-1
Which graph represents the solution to this system of inequalities? y ≤ -2x y &gt-example-2
Which graph represents the solution to this system of inequalities? y ≤ -2x y &gt-example-3
Which graph represents the solution to this system of inequalities? y ≤ -2x y &gt-example-4
User David Parsons
by
2.6k points

2 Answers

14 votes
14 votes

Final answer:

Find the graph that displays y = -2x as a solid line with shading below and y = 3x - 4 as a dashed line with shading above. The intersection of these shadings represents the solution to the system of inequalities.

Step-by-step explanation:

The question involves finding which graph represents the solution to a system of inequalities. The system given is:

  • y ≤ -2x
  • y > 3x - 4

To find the graph representing the solution:

  1. Firstly, graph the line y = -2x. Since the inequality is ≤, this line will be solid, and shading will be below the line, as the y-values are less than or equal to the line's y-values.
  2. Next, graph the line y = 3x - 4. As the inequality is >, this line will be dashed to indicate that points on the line are not included in the solution, and the shading will be above the line because y-values are greater than the y-values on the line.
  3. The region of intersection where the shadings overlap is the solution to the system.

The correct graph will show both inequalities with the respective shadings and a clear intersection of shaded areas.

User Aleksandr Borisov
by
3.6k points
26 votes
26 votes

Answer:

Option A,

Only that graph represents the solution to the given system of inequalities.

Answered by GAUTHMATH

User SoheilYou
by
3.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.