Question

Which graph shows the solution to the system of linear inequalities below? y>2x+1 y<2x-3

Answer 1

Option D: Graph C is the solution to the system of linear inequalities.

Explanation:

The system of linear inequalities are $y \geq 2 x+1$ and $y<-2 x-3$

Let us graph the inequality $y \geq 2 x+1$

Let us substitute the coordinate $(0,0)$ in the inequality $y \geq 2 x+1$, we get,

$0 \geq 2 (0)+1$

$0 \geq1$

This is false. Hence, the solution does not contain the coordinate $(0,0)$

Thus, let us shade the upper part of the line in the graph.

Similarly, let us substitute the coordinate $(0,0)$ in the inequality $y<-2 x-3$, we get,

$0<-2 (0)-3$

$0<-3$

This is false. Hence, the solution does not contain the coordinate $(0,0)$

Thus, let us shade the lower part of the line in the graph.

The solution to the system of linear inequality is the intersection of the two regions.

Thus, the solution of the inequality is Graph C.

Hence, Option D is the correct answer.