Which of the following points is a solution to a system of linear equationsy<3x+5y>-2/3x-3 _a.(3,14)b.(3,9)c.(3,-14)d.(3,-9)

Answer:b) The ONLY solution for the given system is (3,-9).Step-by-step explanation:Here, the given set of equation is:[tex]y< 3 x+5\\y > \frac{-2}{3}x -3[/tex]Now, let us check the given equation  for each given point, we get:(a) For (x, y)  = (3,14)Putting the above values in the given equation y <  3x + 5:  when x  = 3,   3x + 5 = 3(3) + 5 = 14and for y = 14, 14 is NOT LESS THAN 14So, (3,14) is NOT a solution.(b) For (x, y)  = (3,9)Putting the above values in the given equation y <  3x + 5:  when x  = 3,   3x + 5 = 3(3) + 5 = 14and for y = 9,  9 < 14Putting the above values in the given equation y >   -2/3x - 3:  when x  = 3,  [tex]\frac{-2}{3} x -3 = \frac{-2}{3} (3)  -3 = -2 -3  = -5[/tex]and for y = 9,  9 > -5Hence,  (3,9) is a  solution. (c) For (x, y)  = (3,-14)Putting the above values in the given equation y <  3x + 5:  when x  = 3,   3x + 5 = 3(3) + 5 = 14and for y = -14, -14 < 14Putting the above values in the given equation y >   -2/3x - 3:  when x  = 3,  [tex]\frac{-2}{3} x -3 = \frac{-2}{3} (3)  -3 = -2 -3  = -5[/tex]and for y = -14 ,  -14 is NOT GREATER then -5.So, (3,-14) is NOT a solution.(d) For (x, y)  = (3,-9)Putting the above values in the given equation y <  3x + 5:  when x  = 3,   3x + 5 = 3(3) + 5 = 14and for y = -9, -9< 14Putting the above values in the given equation y >   -2/3x - 3:  when x  = 3,  [tex]\frac{-2}{3} x -3 = \frac{-2}{3} (3)  -3 = -2 -3  = -5[/tex]and for y = -14 ,  -9 is NOT GREATER then -5.So, (3,-9) is NOT a solution.Hence, the ONLY solution for the given system is (3,-9)