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.
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