Question

Solve the following system of inequalities graphically :


x + 2y ≤ 10 , x + y ≥ 1 ,x - y ≤ 0 , x ≥ 0 , y ≥ 0​

Answer 1

The linear equation of given inequation x + 2y ≤ 10 is x + 2y = 10

When ,

x = 0 , y = 5

x = 10 , y = 0

Plot the graph of x + 2y = 10

Let a point (0,0) and putting x = 0 and y = 0 in given inequation , we can see that

0 + 2(0) ≤ 10 Which is true

Thus , the solution of x + 2y ≤ 10 is towards with origin (including all the points on the line)

The linear equation of given inequationx + y ≥ 1 is x + y = 1

When ,

x = 0 , y = 1

x = 1 , y = 0

Plot the garph of x + y = 1

Let A point (0,0) and putting x = 0 and y = 0 in given inequation , we can see that

0 + 0 ≥ 1 Which is false

Thus , the solution of x + y ≥ 1 is away from the origin (including all the points on the line)

The linear equation of given inequationx - y ≤ 0 is x - y = 0

When,

x = 0 , y = 0

x = 2 , y = 2

Plot the garph of x - y = 0

Let a point (1,0) and putting x = 1 and y = 0 in given inequation , we can see that

1 - 0 ≤ 0 Which is false

Thus , the solution of x - y ≤ 0 is above the line x - y = 0 (including all the points on the line)

The linear equation of given inequationx ≥ 0 is x = 0

Plot the garph of x = 0

Let a point (1,0) and putting x = 1 in the given inequation , we can see that

1 ≥ 0 Which is true

Thus , the solution of x ≥ 0 is on the right hand side of the line x = 0 (including all the points on the line)

The linear equation of given inequationy ≥ 0 is y = 0

Plot the graph of y = 0

Let a point (0,1) and putting x = 1 in the given inequation , we can see that

1 ≥ 0 Which is true

Thus , the solution of y ≥ 0 is above the line y = 0 (including all the points on the line)

Hence , the common shaded region is the solution of given system of inequalities

Answer 2

Answer:

Solve the following system of inequalities graphically :

x + 2y ≤ 10 , x + y ≥ 1 ,x - y ≤ 0 , x ≥ 0 , y ≥ 0