step by step solution-:

The given inequality:

x-y\gt 2

Replace the inequality by an equal sign:

x-y=2

Find the **x-intercept**:

substitute the **y=0** into the above equation:

x-0=2=>x=2

Find the y-intercept:

substitute the **x=0** into the above equation:

0-y=2=>y=-2

Thus, the coordinates of the **x-intercept** and **y-intercept** are **(2,0)** and **(0,-2)** respectively.

Plot points **(2,0)** and **(0,-2)**.

Draw a dotted line through the points:

Let the test point be **(0,0)**.

x-y\gt 2

Substitute test point **(0,0)** in the above inequality:

0-0\gt 2=>\implies 0>2

The above statement is false:

Since the inequality **x-y>2** holds false for the test point **(0,0)** hence shade the region not containing the test point **(0,0)**.

Similarly, the same procedure in the graph of **6+y<=2x** is shown above.

The graph of the system of inequalities is shown.

\begin{cases}x-y\gt2\\6+y\leq2x\end{cases}

Graph the solution set of the system is shown above.

You may be like this post: