MATH SOLVE

5 months ago

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

Accepted Solution

A:

Answer-First graph represents the system of linear inequalities.Solution-The system of linear inequalities are,[tex]y<3x+1\\\\y\geq-2x-4[/tex]Considering them as equalities,[tex]y=3x+1[/tex] ---------------1[tex]y=-2x-4[/tex] -----------2Subtracting both equations,[tex]\Rightarrow 0=3x+1+2x+4[/tex][tex]\Rightarrow 5x+5=0[/tex][tex]\Rightarrow 5x=-5[/tex][tex]\Rightarrow x=-1[/tex]Putting the value of x in equation 1,[tex]y=3(-1)+1=-2[/tex]So, the point of intersection is (-1, -2)Taking the point as origin and putting it in inequality 1,[tex]\Rightarrow 0<3(0)+1[/tex][tex]\Rightarrow 0<1[/tex]As it satisfies, so the shaded region will be towards origin.Taking the point as origin and putting it in inequality 2,[tex]\Rightarrow 0\geq-2(0)-4[/tex][tex]\Rightarrow 0\geq-4[/tex]As it satisfies, so the shaded region will be towards origin.From above, option has the correct graph.