Questions: Pretest: Unit 5 Which graph shows the solution to this system of linear inequalities? y ≥ 2x+1 y < -2x-3

Transcript text: Pretest: Unit 5 Which graph shows the solution to this system of linear inequalities? \[ \begin{array}{l} y \geq 2 x+1 \\ y<-2 x-3 \end{array} \]

Solution

Solution Steps

Step 1: Identify the inequalities

The given system of linear inequalities is: \[ y \geq 2x + 1 \] \[ y < -2x - 3 \]

Step 2: Graph the first inequality

Graph the line \( y = 2x + 1 \). Since the inequality is \( y \geq 2x + 1 \), shade the region above the line.

Step 3: Graph the second inequality

Graph the line \( y = -2x - 3 \). Since the inequality is \( y < -2x - 3 \), shade the region below the line.

Step 4: Identify the overlapping region

The solution to the system of inequalities is the region where the shaded areas of both inequalities overlap.

Final Answer

The graph that shows the solution to the system of linear inequalities is Graph D.

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