12.x-2y3, 3x + 4y12, x20,y21

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Solution

The inequalities are,

x−2y≤3, 3x+4y≥12, y≥1 and x≥0.

For the inequality,

x−2y≤3(1)

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

0−2y=3 y=− 3 2 =−1.5

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

x−2( 0 )=3 x=3

For the inequality,

3x+4y≥12(2)

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

3( 0 )+4y=12 y=3

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

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

For the inequality,

y≥1(3)

Represents the region above the line y=1.

For the inequality,

x≥0(4)

Represent the region on the right hand side of y−axis.

From all the four inequalities the graph is shown as,

Thus, in the graph the dark blue color represent the graph of the system of the all four inequalities.

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