Solve the following systems of inequalities graphically:

$3 x + 4 y \leq 60, x + 3 y \leq 30, x \geq 0, y \geq 0$

Open in App

Solution

The given inequality is $3 x + 4 y \leq 60$ .

Draw the graph of the line 3x +4y =60.

Table of values satisfying the equation

3x +4y =60

$\begin{matrix} x & 8 & 12 y & 9 & 6 \end{matrix}$

Putting (0,0) in the given inequation, we have $3 \times 0 + 4 \times 0 \leq 60 \Rightarrow 0 \leq 60$ , which is true.

$∴$ Half plane of $3 x + 4 y \leq 60$ is towards origin.

Also the given inequality is $x + 3 y \leq 30$ .

Draw the graph of the line x+3y =30.

Table of values satisfying the equation

x+3y =30

$\begin{matrix} x & 0 & 9 y & 10 & 7 \end{matrix}$

Putting (0,0) in the given inequation, we have $0 + 3 \times 0 \leq 30 \Rightarrow 0 \leq 30$ , which is true.

$∴$ Half plane of $x + 3 y \leq 30$ is towars origin.

Suggest Corrections

Similar questions

Solve the following system of inequalities graphically: 3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0

Solve the following system of inequalities graphically: 3x + 2y ≤ 150, x + 4y ≤ 80, x ≤ 15, y ≥ 0, x ≥ 0

3 x + 2 y \leq 150, x + 4 y \leq 80, x \leq 15, y \geq 0, x \geq 0

Solve the following systems of inequalities graphically:

$4 x + 3 y \leq 60, y \geq 2 x, x \geq 3, x, y \geq 0$

[[Q]]

Solve the following system of inequalities graphically:

4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x, y ≥ 0

Join BYJU'S Learning Program