Question

15. x +2)' < 10, x + y > 1, 0, x > 0, y 20

Answer 1

The given inequalities are,

x+2y≤10(1)

x+y≥1(2)

x−y≤0(3)

x≥0;y≥0

Substitute 0 for x in equation (1).

0+2y=10 y=5

Substitute 0 for y in equation (1).

x+0=10 x=10

Substitute 0 for x and y in equation (1)

0+0≤10 0≤10

The above inequality is true because 0 is always less than 10, so the graph of this inequality will be toward the origin.

The coordinates of inequality (1) are ( 0,5 ),( 10,0 ).

Substitute 0 for x in equation (2).

0+y=1 y=1

Substitute 0 for y in equation (2).

x+0=1 x=1

Substitute 0 for x and y in equation (2)

0+0≥1 0≥1

The above inequality is false because 0 is never greater than 1, so the graph of this inequality will be away from the origin.

The coordinates of the inequality (2) are ( 0,1 ),( 1,0 ).

Substitute 0 for x in equation (3).

0−y=0 y=0

Substitute 0 for y in equation (3).

x−0=0 x=0

Substitute 0 for x and y in equation (3),

0−0≤0 0≤0

The above inequality is true because 0 is equal to 0, so the graph of this inequality will be toward the origin.

The coordinates of the inequality (3) are ( 0,0 ),( 0,0 ).

Draw the graph of the lines x+2y≤10, x+y≥1, x−y≤0 using their coordinates.

Figure (1)

Figure (1) shows the graph of the lines x+2y≤10, x+y≥1, x−y≤0 where red color represents, x+2y≤10, blue color represents x+y≥1 and green color represents x−y≤0.

Since x≥0 and y≥0, therefore every point in the graph lies in the first quadrant.