Question

Which ordered pairs are in the solution set of the system of linear inequalities? y > x y < x + 1 (5, –2), (3, 1), (–4, 2) (5, –2), (3, –1), (4, –3) (5, –2), (3, 1), (4, 2) (5, –2), (–3, 1), (4, 2)

Answer 1

None

Explanation:

We are given that two inequality equations

`y >x`...(I Equation )

`y < x+1`...( II equation )

If we substituting the value of point (5,-2) in equation I

x=5, y=-2

Then
`-2 \\gtr 5`

It is not true because a negative number is always smaller than the positive number

So it is not possible for solution of system of inequality .

Now, x=3, y= 1 substituting in equation I

Then ,
`1\\grt 3`

Therefore, the value is not possible and it is not a solution of system of equation.

Now, substituting x=-4,y=2

2 > -4

Therefore, is true for equation I

`2\\less -3`

It is note true for equation II

Hence, the point (-4, 2 ) is not a solution of system of inequality equation.

x=5, y= -2 substituting in equation I

`-2\\gtr 5`

It is not true for equation I

Hence, it is not a solution of system of inequality equation.

x=3, y= -1

`-1\\gtr 3` it is not true for equation I

It is not a solution for system of inequality equations.

x=4,y=-3

It is not true for equation I

Therefore, it is not a solution of system of inequality equations.

x=5,y=-2

It is not true for equation I

Hence, it is not a solution of system of inequalities.

x=3, y=1

Substituting in equation I

`1\\gtr 3`

Therefore, it is not a solution of system of inequalties.

From we can see that the graph of two lines do not cut anywhere to each other . Therefore, no point is the solution of system of inequality equations.

Answer : None

Answer 2

None

Explanation:

(1) y > x

(2) y < x + 1

Satisfy (1) but not (2)

(-4, 2)

(-3, 1)

Satisfy (2) but not (1)

(3, 1)

(3, -1)

(4, 2)

(4, -3)

(5, -2)

Satisfy both (1) and (2)

None

The solution set is empty.