Solve the following system of inequalities graphically: \[5x+4y\le 20\], \[x\ge 1\], \[y\ge 2\]

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Solve the following system of inequalities graphically:

$5x+4y\le 20$

,

$x\ge 1$

,

$y\ge 2$

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

Solve the following system of inequalities graphically:

$5x+4y\le 20$

,

$x\ge 1$

,

$y\ge 2$

Solution:

The given inequalities are

$5x+4y\le 20$

,

$x\ge 1$

,

$y\ge 2$

For

$5x+4y\le 20$

,

Let us put value of

$x=0$

and

$y=0$

in equation one by one, we get

$y=5$

and

$x=4$

We get the required points as

$(0,5)$

and

$(4,0)$

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

$(0,0)$

$0\le 20$

Which is true, hence the origin would lie in the solution area. The required area of the line`s graph is on the left side of the graph.

Now we have

$x\ge 1$

,

So for all the values of y, x would be

$1$

,

We get the required points as

$(1,0)$

,

$(1,2)$

and so on.

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

$(0,0)$

$0\ge 1$

, which is not true

Therefore, the origin would not lie in the required area. The required area on the graph will be on the right side of the line`s graph.

Now consider

$y\ge 2$

,Similarly for all the values of x, y would be

$2$

.

We get the required points as

$(0,2)$

,

$(1,2)$

and so on.

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

$(0,0)$

$0\ge 2$

, which is not true

Therefore the required area would be on the right side of the line`s graph.

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

i

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More Material

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