2. 3x + 2ys 12, x2 1, y 2 2

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Solution

The inequalities are,

3x+2y ≤ 12, x ≥1, y≥2.

For the inequality,

3x+2y ≤ 12(1)

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

3( 0 )+2y=12 2y=12 y=6

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

3x+2( 0 )=12 3x=12 x= 4

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

For the inequality y ≥2, the value of y can be equal to 2 or 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 blue color, and the inequality 3x+2y ≤ 12 is shown by green color.

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

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