What graph represents the system of linear inequalities? y<3x+1 y≥−2x−4

Question

asked Nov 9, 2018 188k views

2 Answers

Aatifh · Answer 1 · 2018-11-13T12:34:09+0000

Answer-

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.