Question

solve the following system or inequalities graphically
3x+2y≤150,x+4y≤80,x≤15,x≥0,y≥0​

Answer 1

$\rm :\longmapsto\:3x + 2y = 150$

Let sketch this line.

On substituting x = 0, we get

3× 0 + 2y = 150

0 + 2y = 150

y = 75

On substituting y = 0, we get

3x + 0 = 150

3x = 150

x = 50

$\rm :\longmapsto\:x + 4y = 80$

On substituting x = 0, we get

0 + 4y = 80

4y = 80

y = 20

On substituting y = 0, we get

x + 0 = 80

x = 80

$\rm :\longmapsto\:x = 15$

A line parallel to x - axis passes through (15, 0).

Answer 2

EXPLANATION.

Inequalities graphically.

⇒ 3x + 2y ≤ 150. - - - - - (1).

⇒ x + 4y ≤ 80. - - - - - (2).

⇒ x ≤ 15. - - - - - (3).

⇒ x ≥ 0. and y ≥ 0.

As we know that,

We can write equation as.

⇒ 3x + 2y = 150. - - - - - (1).

⇒ x + 4y = 80. - - - - - (2).

⇒ x = 15. - - - - - (3).

From equation (1), we get.

⇒ 3x + 2y = 150. - - - - - (1).

Put the value of x = 0 in the equation, we get.

⇒ 3(0) + 2y = 150.

⇒ 2y = 150.

⇒ y = 75.

Their Co-ordinates = (0,75).

Put the value of y = 0 in the equation, we get.

⇒ 3x + 2(0) = 150.

⇒ 3x = 150.

⇒ x = 50.

Their Co-ordinates = (50,0).

From equation (2), we get.

⇒ x + 4y = 80. - - - - - (2).

Put the value of x = 0 in the equation, we get.

⇒ (0) + 4y = 80.

⇒ 4y = 80.

⇒ y = 20.

Their Co-ordinates = (0,20).

Put the value of y = 0 in the equation, we get.

⇒ x + 4(0) = 80.

⇒ x = 80.

Their Co-ordinates = (80,0).

From equation (3), we get.

⇒ x = 15.

Their Co-ordinates = (15,0).