9. 5x 4y 20, x2 1, y22

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Solution

The inequalities are,

5x+4y ≤ 20, x ≥ 1, y ≥ 2.

For the inequality,

5x+4y ≤ 20(1)

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

5( 0 )+4y = 20 4y = 20 y = 5

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

5x+4( 0 ) = 20 5x = 20 x = 4

For the inequality x ≥1, the value of x can be equal to 1 and greater than 1.

For the inequality y ≥2, the value of y can be equal to 2 and greater than 2.

For all the three inequalities, the graph is shown as,

In the graph, the inequality x ≥1 is shown by red color, the inequality y ≥2 is shown by green color, and the inequality 5x+4y ≤ 20 is shown by blue color.

Thus, the region ABC as shown in the graph is the graph of the system of all three inequalities.

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