Solve the following system of inequalities graphically: \[3x+2y\le 150\], \[x+4y\le 80\], \[x\le 5\], \[y\ge 0,x\ge 0\]

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Solve the following system of inequalities graphically:

$3x+2y\le 150$

,

$x+4y\le 80$

,

$x\le 5$

,

$y\ge 0,x\ge 0$

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

Solve the following system of inequalities graphically:

$3x+2y\le 150$

,

$x+4y\le 80$

,

$x\le 5$

,

$y\ge 0,x\ge 0$

Solution:

The given inequalities are

$3x+2y\le 150$

,

$x+4y\le 80$

,

$x\le 5$

,

$y\ge 0,x\ge 0$

For

$3x+2y\le 150$

Let us put value of

$x=0$

and

$y=0$

in equation one by one, we get

$y=75$

and

$x=50$

We get the required points as

$(0,75)$

and

$(50,0)$

To check if the origin is included in the line`s graph

$(0,0)$

$0\le 150$

, which is true

Therefore, the solution area for the line would be on the left side of the line`s graph which would be including the origin too.

For

$x+4y\le 80$

,

Let us put value of

$x=0$

and

$y=0$

in equation one by one, we get

$y=20$

and

$x=80$

We get the required points as

$(0,20)$

and

$(80,0)$

To check if the origin is included in the line`s graph

$(0,0)$

$0\le 80$

, which is also true, so the origin lies in the solution area.

Therefore, the required solution area would be toward the left of the line`s graph.

For

$x\le 5$

,

There is no change in x values for all values of y.

To check if the origin is included in the line`s graph

$(0,0)$

$0\le 15$

,which is true so the origin would be included in the solution area. The required solution area would be towards the left of the line`s graph.

For

$y\ge 0,x\ge 0$

The solution would lie in the quadrant(Since x and y are greater than

$0$

)

In the below graph the shaded area in the graph is the required solution of the given inequalities.

i

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