Solve the following system of inequalities graphically: \[2x+y\ge 6,3x+4y\le 12\] - Noon Academy

Solve the following system of inequalities graphically:

$2x+y\ge 6,3x+4y\le 12$

Class 11 | Exercise 6.2 | Linear Inequalities | Maths | NCERT

Solve the following system of inequalities graphically:

$2x+y\ge 6,3x+4y\le 12$

Solution:

The given inequalities are

$2x+y\ge 6$

…………… (i)

$3x+4y\le 12$

……………. (ii)

For

$2x+y\ge 6$

Take value of

$x=0$

and

$y=0$

in equation one by one, we get value of

$y=6$

and

$x=3$

We got the point as

$(0,6)$

and

$(3,0)$

Let us check for

$(0,0)$

We got

$0\ge 6$

which is not true, hence the origin does not lies in the solution of the equality. The required region is on the right side of the graph.

For

$3x+4y\le 12$

Take value of

$x=0$

and

$y=0$

one by one in equation, We get value of

$y=3$

and

$x=4$

We got the points as

$(0,3)$

,

$(4,0)$

Let us check for origin

$(0,0)$

We got

$0\le 12$

which is true,

Therefore, the origin lies in solution of the equation.

We can say that the region on the right of the equation is the region required.

In the below graph the shaded region is the required region.

i

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