Solve the following system of inequalities graphically: \[x+y\ge 4,2x-y<0\] - Noon Academy

Solve the following system of inequalities graphically:

$x+y\ge 4,2x-y<0$

Class 11 | Exercise 6.3 | Linear Inequalities | Maths | NCERT

Solve the following system of inequalities graphically:

$x+y\ge 4,2x-y<0$

Solution:

The given inequalities are

$x+y\ge 4,2x-y<0$

For

$x+y\ge 4$

Let us put the value of

$x=0$

and

$y=0$

in equation one by one, we get

$y=4$

and

$x=4$

Therefore, we got points as

$(0,4)$

and

$(4,0)$

Now check for the origin

$(0,0)$

We got

$0\ge 4$

,which is not true.

We can say that the origin would not lie in the solution area. The required region would be on the right of line`s graph.

Now for

$2x-y<0$

Let us put the value of

$x=0$

and

$y=0$

in equation one by one, we get

$y=0$

and

$x=0$

Let us take

$x=1$

we get

$y=2$

Therefore, the points for the given inequality are

$(0,0)$

and

$(1,2)$

As we can see that the origin lies on the given equation

Now we will check for

$(4,0)$

point to check which side of the line`s graph will be included in the solution.

We get

$8<0$

which is not true

Therefore, the required region would be on the left side of the line

$2x-y<0$

In the below graph the shaded region is the required solution of the inequalities.

i

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