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

b) The ONLY solution for the given system is (3,-9).

Step-by-step explanation:

Here, the given set of equation is:

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 = 14

and for y = 14, 14 is NOT LESS THAN 14

So, (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 = 14

and for y = 9,  9 < 14

Putting the above values in the given equation y >   -2/3x - 3:  

when x  = 3,  

and for y = 9,  9 > -5

Hence,  (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 = 14

and for y = -14, -14 < 14

Putting the above values in the given equation y >   -2/3x - 3:  

when x  = 3,  

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 = 14

and for y = -9, -9< 14

Putting the above values in the given equation y >   -2/3x - 3:  

when x  = 3,  

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)

because they could drop even lower..