Question

Solve the following system of inequality graphically: x+y>=4, 2x-y>0

Answer 1

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Answer 2

SOLUTION :

The linear equations of given inequations x + y >= 4 is x + y = 4

When ,

x = 0 , y = 4

x = 4 , y = 0

The linear equations of given inequations 2x - y > 0 is 2x - y = 0

When ,

x = 1 , y = 2

x = 0 , y = 0

Now , plot the graph of x + y = 4 and 2x - y = 0

Let a point (0,0) and putting x = 0 and y = 0 in given inequality x + y >= 4 , we can see that

0 + 0 >= 4 Which is false

Thus , the solution of x + y >= 4 is away from origin (including every points on the line)

Let a point (1,0) and putting x = 1 and y = 0 in given inequality 2x - y > 0 , we can see that

2(1) - (0) > 0 Which is true

Thus , the solution of 2x - y > 0 is below the line 2x - y = 0

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