Respuesta :
Answer:
Correct graph is C
Step-by-step explanation:
Given two inequalities are:
1. [tex]y\leq -3x+1[/tex]
2. [tex]y\leq x+3[/tex]
Step1 : Remove the inequalities
1. [tex]y=-3x+1[/tex]
2. [tex]y=x+3[/tex]
Step2 : Finding intersection points of equations
By solving linear equation
[tex]y=-3x+1=x+3[/tex]
[tex]-3x+x+3[/tex]
[tex]x=-0.5[/tex]
Replacing value of x in any equations
we get,
[tex]y=x+3\\[/tex]
[tex]y=-0.5+3[/tex]
[tex]y=2.5[/tex]
Therefore, Point of intersection is (-0.5,2.5)
Step3: Test of origin (0,0)
Here, If inequalities holds true for origin then, shades the graph towards the origin.
For equation 1.
[tex]y\leq -3x+1[/tex]
[tex]0\leq -3(0)+1[/tex]
[tex]0\leq +1[/tex]
True, Shade graph towards origin.
For equation 2.
[tex]y\leq x+3[/tex]
[tex]0\leq 0+3[/tex]
[tex]0\leq 3[/tex]
True, Shade graph towards origin.
Thus, Correct graph is C