91Ó°ÊÓ

We are given an inequality $2x-y>3$. We are suppose to draw the graph representing this inequality.

• If the inequality has $â‰\yen$or $≤$in it, then the boundary line of the graph is solid.
• If the inequality has $>$or $<$in it, then the boundary line of the graph is dashed.

The given inequality is$2x-y>3$

We will first replace the inequality sign $>$with an equal sign. After this, we have the equation $2x-y=3$.

Since the inequality has $>$, we note that the boundary line of the graph must be dashed.

Thus the graph is,

Consider a point that is not on the boundary line. Let us take $(-1,1)$.

Here, $x=-1,y=1$.

We will substitute these values in the inequality $2x-y>3$and check if the point $(-1,1)$is a solution to the given inequality.

$$\begin{gathered} 2x-y>3 \\ 2(-1)-1>3 \\ -2-1>3 \\ -3>3 \end{gathered}$$

which is false.

Therefore, the point $(-1,1)$is not a solution for the given inequality.

Since the point $(-1,1)$ is not a solution for the inequality $2x-y>3$, we have to shade the side of the boundary line that is opposite to the side containing the point $(-1,1)$.

Therefore, the graph is

All the points in the shaded region, except for those on the boundary line represent the solution for the inequality$2x-y>3$.

The graph of the inequality $2x-y>3$is