Question

Which graph shows the solution set as a purple overlap to the given system of inequalities ?

Answer 1

Given,

The system of inequalities are

`\begin{gathered} y\leq2x+3 \\ y\ge-x+4 \end{gathered}`

The region for the system y <= 2x+3 is,

Take x = 0,

`\begin{gathered} \text{ At x =0} \\ y\le2x+3 \\ y\le2(0)+3 \\ y\le3 \\ At\text{ x = 1} \\ y\le2(1)+3 \\ y\le5 \\ At\text{ x = -1} \\ y\le2(-1)+3 \\ y\le1 \end{gathered}`

The coordinates of point thorugh the line of inequality pass is (0, 3), (1, 5) and (-1, 1).

The region for the system y >= -x+4 is,

Take x = 0,

`\begin{gathered} \text{ At x =0} \\ y\ge-x+4 \\ y\ge-(0)+4 \\ y\ge4 \\ At\text{ x = 1} \\ y\ge-(1)+4 \\ y\ge3 \\ At\text{ x = -1} \\ y\ge-(-1)+4 \\ y\ge5 \end{gathered}`

The coordinates of point thorugh the line of inequality pass is (0, 4), (1, 3) and (-1, 5).

The graph is,

Hence, Graph C is correct option.