Solve the following system of inequalities graphically: 5x + 4y ≤ 20, x ≥ 1, y ≥ 2

Asked by Abhisek | 1 year ago |  105

##### Solution :-

Given 5x + 4y ≤ 20,

Putting value of x = 0 and y = 0 in equation one by one, we get value of

y = 5 and x= 4

The required points are (0, 5) and (4, 0)

Checking if the origin lies in the solution area (0, 0)

0 ≤ 20

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

We have x ≥ 1,

For all the values of y, x would be 1,

The required points would be (1, 0), (1, 2) and so on.

Checking for origin (0, 0)

0 ≥ 1, which is not true

So the origin would not lie in the required area. The required area on the graph will be on the right side of the lines graph.

Consider y ≥ 2

Similarly for all the values of x, y would be 2.

The required points would be (0, 2), (1, 2) and so on.

Checking for origin (0, 0)

0 ≥ 2, this is no true

Hence the required area would be on the right side of the lines graph.

The shaded area on the graph shows the required solution of the given inequalities.

Answered by Pragya Singh | 1 year ago

### Related Questions

#### Solve each of the following in equations and represent the solution set on the number line

Solve each of the following in equations and represent the solution set on the number line $$\dfrac{5x}{4}-\dfrac{4x-1}{3}>1,$$ where x ϵ R.

#### Solve each of the following in equations and represent the solution set on the number line.

Solve each of the following in equations and represent the solution set on the number line.$$\dfrac{5x-8}{3}\geq \dfrac{4x-7}{2}$$, where x ϵ R.

#### Solve each of the following in equations and represent the solution set on the number line. 3 – 2x ≥ 4x – 9,

Solve each of the following in equations and represent the solution set on the number line. 3 – 2x ≥ 4x – 9, where x ϵ R.

#### Solve each of the following in equations and represent the solution set on the number line. 3x – 4 > x + 6

Solve each of the following in equations and represent the solution set on the number line. 3x – 4 > x + 6, where x ϵ R.