Question

What graph represents the system of linear inequalities?

y<3x+1
y≥−2x−4

Answer 1

First one

Explanation:

Answer 2

First graph represents the system of linear inequalities.

Solution-

The system of linear inequalities are,

`y<3x+1\\\\y\geq-2x-4`

Considering them as equalities,

`y=3x+1` ---------------1

`y=-2x-4` -----------2

Subtracting both equations,

`\Rightarrow 0=3x+1+2x+4`

`\Rightarrow 5x+5=0`

`\Rightarrow 5x=-5`

`\Rightarrow x=-1`

Putting the value of x in equation 1,

`y=3(-1)+1=-2`

So, the point of intersection is (-1, -2)

Taking the point as origin and putting it in inequality 1,

`\Rightarrow 0<3(0)+1`

`\Rightarrow 0<1`

As it satisfies, so the shaded region will be towards origin.

Taking the point as origin and putting it in inequality 2,

`\Rightarrow 0\geq-2(0)-4`

`\Rightarrow 0\geq-4`

As it satisfies, so the shaded region will be towards origin.

From above, option has the correct graph.