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Which graph represents the following system of inequalities?

Which graph represents the following system of inequalities?-example-1
Which graph represents the following system of inequalities?-example-1
Which graph represents the following system of inequalities?-example-2

2 Answers

5 votes

Answer:

D

Explanation:

On graphing the 3 equations, we find that the central area (triangle) formed by the 3 inequalities is the solution.

Which graph represents the following system of inequalities?-example-1
User Whossname
by
9.0k points
2 votes

Answer:

D

Explanation:

When graphing inequalities:

  • < or > : dashed lines
  • ≤ or ≥ : solid line
  • < or ≤ : shading under the line
  • > or ≥ : shading above the line

Given inequalities:


\begin{cases}y > (1)/(2)x-1\\\\y\leq -x+1\\\\y > -2x-1 \end{cases}

From inspection of the given graphs, the red dashed line is the first inequality as it is the only inequality with a positive slope.

The blue sold line is the second inequality, as it is the only inequality with the sign that suggest a solid line.

Therefore, by process of elimination, the green dashed line is the third inequality.

Using the inequality signs and their definitions for shading, find the graph that has:

  • Shading above the red dashed line
  • Shading below the blue solid line
  • Shading above the green dashed line

The only graph that matches these conditions is graph D

Which graph represents the following system of inequalities?-example-1
User Slugslog
by
7.6k points

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