Solve the following simultaneous linear inequations graphically. $x + 2 y \leq 10, x + y \leq 6, x \leq 4, x \geq 0 a n d y \geq 0$

Open in App

Solution

We draw the graph of the lines $x + 2 y = 10, x + y = 6 a n d x = 4$

Table for line $x + 2 y = 10$ or $y = \frac{10 - x}{2}$ is

$\begin{matrix} x & 0 & 10 y & 5 & 0 \end{matrix}$

On putting (0, 0) in the inequality $x + 2 y \leq 10,$ we get $0 + 0 \leq 10$ (true). So, the inequality lies towards the origin.

table for line $x + y = 6$ or $y = 6 - x$ is [1]

$\begin{matrix} x & 0 & 6 y & 6 & 0 \end{matrix}$

On putting (0, 0) in the inequality $x + y \leq 6,$ we get $0 + 0 \leq 6$ (true). So, the inequality lies towards the origin.

Line $x = 4$ is the perpendicular line on the x-axis at a distance of 4 units from origin. [1]

Also, $x \geq 0, y \geq 0,$ so every point of the shaded region lie in the first quadrant.

Now, plot all the points of the inequalities on a graph paper which are shown below [1]

[1]

Suggest Corrections

Similar questions

Q. Solve the following systems of inequations graphically:

x - 2 y \leq 2, x + y \geq 3, - 2 x + y \leq 4, x \geq 0, y \geq 0

Solve the following system of inequalities graphically: x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0

Q. Solve the given inequalities graphically:

x + 2 y \leq 10, x + y \geq 1, x - y \leq 0, x \geq 0, y \geq 0

Q. Solve the following systems of linear inequations graphically:

(i) 2x + 3y ≤ 6, 3x + 2y ≤ 6, x ≥ 0, y ≥ 0
(ii) 2x + 3y ≤ 6, x + 4y ≤ 4, x ≥ 0, y ≥ 0
(iii) x − y ≤ 1, x + 2y ≤ 8, 2x + y ≥ 2, x ≥ 0, y ≥ 0
(iv) x + y ≥ 1, 7x + 9y ≤ 63, x ≤ 6, y ≤ 5, x ≥ 0, y ≥ 0
(v) 2x + 3y ≤ 35, y ≥ 3, x ≥ 2, x ≥ 0, y ≥ 0

Solve the following systems of linear inequations graphically :

$(i) 2 x + 3 y \leq 6, 3 x + 2 y \leq 6, x \geq 0, y \geq 0 (i i) 2 x + 3 y \leq 6, x + 4 y \leq 4, x \geq 0, y \geq 0 (i i i) x + y \geq 1, x + 2 y \leq 8, 2 x + y \geq 2, x \geq 0, y \geq 0 (i v) x + y \geq 1, 7 x + 9 y \leq 63, y \leq 5, x \geq 0, y \geq 0 (v) 2 x + 3 y \leq 35, y \geq 3, x \geq 2, x \geq 0, y \geq 0$

Join BYJU'S Learning Program

Solve the following simultaneous linear inequations graphically. x+2y≤10, x+y≤6, x≤4, x≥0 and y≥0

Solve the following simultaneous linear inequations graphically. $x + 2 y \leq 10, x + y \leq 6, x \leq 4, x \geq 0 a n d y \geq 0$