Respuesta :
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 = 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, [tex]\frac{-2}{3} x -3 = \frac{-2}{3} (3) -3 = -2 -3 = -5[/tex]
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, [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 = 14
and for y = -9, -9< 14
Putting 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)
