Represent solution set of each of the following inequations graphically in two dimensional plane:

Question 1: x + 2y - 4 \leq 0

Answer:

To draw the equation, we calculate the intercepts:

x = 0 y = 2 y axis intercept = (0,2)
x=4 y=0 x axis intercept = ( 4, 0)

To find out which side of the line the solution lies. We do a test of inequality.

If we substitute ( 0,0) in the equation we see that -4 \leq 0 which is true.

Hence,  (0, 0) lies in the region that satisfies the inequation.155-1(a1)\\

Question 2: x + 2y \geq 6

Answer:

To draw the equation, we calculate the intercepts:

x = 0 y = 3 y axis intercept = (0,3)
x=6 y=0 x axis intercept = ( 6, 0)

To find out which side of the line the solution lies. We do a test of inequality.

If we substitute ( 0,0) in the equation we see that 0 \geq 6 which is not true.

Hence,  (0, 0) does not lies in the region that satisfies the inequation. Hence the solution is on the other side of the line.155-2(a)\\

Question 3: x + 2 \geq 0

Answer:155-4(a)\\

Question 4: x - 2y < 0

Answer:

To draw the equation, we calculate the intercepts:

x = 4 y = 2 y axis intercept = (4, 2)
x=-6 y=-3 x axis intercept = ( -6, -3)

To find out which side of the line the solution lies. We do a test of inequality.

If we substitute ( 1,1) in the equation we see that -1 < 0 which is true.

Hence,  (1, 1) lies in the region that satisfies the inequation. Hence the solution is on this side of the line.155-4x\\

Question 5: -3 x + 2y \leq 6

Answer:

To draw the equation, we calculate the intercepts:

x = 0 y = 3 y axis intercept = (0,3)
x=-2 y=0 x axis intercept = ( -2, 0)

To find out which side of the line the solution lies. We do a test of inequality.

If we substitute ( 0,0) in the equation we see that 0 \leq 6 which is true.

Hence,  (0, 0) lies in the region that satisfies the inequation.155-5(a)\\

Question 6: x \leq 8 - 4y

Answer:

To draw the equation, we calculate the intercepts:

x = 0 y = 2 y axis intercept = (0,2)
x=8 y=0 x axis intercept = ( 8, 0)

To find out which side of the line the solution lies. We do a test of inequality.

If we substitute ( 0,0) in the equation we see that 0 \leq 8 which is true.

Hence,  (0, 0) lies in the region that satisfies the inequation.155-6(a)\\

Question 7:  0 \leq 2x-5y+10

Answer:

To draw the equation, we calculate the intercepts:

x = 0 y = 2 y axis intercept = (0,2)
x=-5 y=0 x axis intercept = ( -5, 0)

To find out which side of the line the solution lies. We do a test of inequality.

If we substitute ( 0,0) in the equation we see that 0 \leq 10 which is true.

Hence,  (0, 0) lies in the region that satisfies the inequation.155-7(a)\\

Question 8: 3y > 6 - 2x

Answer:

To draw the equation, we calculate the intercepts:

x = 0 y = 2 y axis intercept = (0, 2)
x=3 y=0 x axis intercept = ( 3,0)

To find out which side of the line the solution lies. We do a test of inequality.

If we substitute ( 0,0) in the equation we see that 0 > 6 which is not true.

Hence,  (0, 0) does not lies in the region that satisfies the inequation. Hence the solution is on the other side of the line.155-8(a)\\

Question 9: y > 2x-8

Answer:

To draw the equation, we calculate the intercepts:

x = 0 y = -8 y axis intercept = (0,-8)
x=4 y=0 x axis intercept = ( 4, 0)

To find out which side of the line the solution lies. We do a test of inequality.

If we substitute ( 0,0) in the equation we see that 0 > -8 which is true.

Hence,  (0, 0) lies in the region that satisfies the inequation.155-9(a)\\

Question 10: 3x-2y \leq x+y - 8

Answer:

To draw the equation, we calculate the intercepts:

x = 0 y = \frac{8}{3} y axis intercept = (0, \frac{8}{3})
x=-4 y=0 x axis intercept = ( -4,0)

To find out which side of the line the solution lies. We do a test of inequality.

If we substitute ( 0,0) in the equation we see that 0 \leq -8 which is not true.

Hence,  (0, 0) does not lies in the region that satisfies the inequation. Hence the solution is on the other side of the line.155-10(a)\\