Question

5. 2x - y >1, x 2y-1

Answer 1

The inequalities are,

2x−y> 1, x−2y <−1

For the inequality,

2x−y> 1(1)

Put the value x=0 in equation (1).

2( 0 )−y = 1 y=−1

Put the value y = 0 in equation (1).

2x−( 0 )=1 x=0.5

For the inequality,

x−2y < −1(2)

Put the value x=0 in equation (2).

( 0 )−2y =−1 y=0.5

Put the value y=0 in equation (2).

x−2( 0 )=−1 x=−1

For the two inequalities, the graph is shown as:

In the graph, the inequality 2x−y >1 is shown by red color and the inequality x−2y< −1 is shown by blue color.

Thus, in the graph, the shaded region above point A with both the (blue + red) colors is the graph of the systems of both the inequalities.