please help! Which of the following points lie in the solution set to the following system of inequalities?y < −3x + 3y < x + 2 (1, −5) (1, 5) (5, 1) (−1, 5)
Accepted Solution
A:
Answer:(1,-5)Step-by-step explanation:The given system of inequalities are;[tex]y\:<\:-3x+3[/tex]and[tex]y\:<\:x+2[/tex]The point that is a solution will satisfy the two inequalities.Checking for (1,-5)[tex]-5\:<\:-3(1)+3[/tex] and [tex]-5\:<\:1+2[/tex][tex]-5\:<\:0[/tex]: True [tex]-5\:<\:3[/tex] : TrueThis point lies in the solution region.Checking for (1,5)[tex]5\:<\:-3(1)+3[/tex] and [tex]5\:<\:1+2[/tex][tex]5\:<\:0[/tex]: False [tex]5\:<\:3[/tex] : FalseThis point does not lie in the solution region.Checking for (5,1)[tex]1\:<\:-3(5)+3[/tex] and [tex]1\:<\:5+2[/tex][tex]1\:<\:-12[/tex]: False [tex]1\:<\:7[/tex] : TrueThis point does not lie in the solution region.Checking for (-1,5)[tex]5\:<\:-3(-1)+3[/tex] and [tex]5\:<\:-1+2[/tex][tex]5\:<\:6[/tex]: True [tex]5\:<\:1[/tex] : FalseThis point does not lie in the solution region.