Use the image to answer the question.

Question

A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. 2 dashed lines with arrows at both ends are plotted, and various regions of the graph are marked.

Which point is a solution to the simultaneous inequalities y<12x and y>13x+3 ?

(1 point)
Responses

(25,12)
left parenthesis 25 comma 12 right parenthesis

(10,5)
left parenthesis 10 comma 5 right parenthesis

(3,6)
left parenthesis 3 comma 6 right parenthesis

(2,2)

Answer 1

To determine which point is a solution to the simultaneous inequalities \( y < 12x \) and \( y > 13x + 3 \), we need to evaluate each point against both inequalities.

1. Point (25, 12):

   • For \( y < 12x \):
     • \( 12 < 12(25) \)
     • \( 12 < 300 \) (True)
   • For \( y > 13x + 3 \):
     • \( 12 > 13(25) + 3 \)
     • \( 12 > 325 + 3 \)
     • \( 12 > 328 \) (False)

2. Point (10, 5):

   • For \( y < 12x \):
     • \( 5 < 12(10) \)
     • \( 5 < 120 \) (True)
   • For \( y > 13x + 3 \):
     • \( 5 > 13(10) + 3 \)
     • \( 5 > 130 + 3 \)
     • \( 5 > 133 \) (False)

3. Point (3, 6):

   • For \( y < 12x \):
     • \( 6 < 12(3) \)
     • \( 6 < 36 \) (True)
   • For \( y > 13x + 3 \):
     • \( 6 > 13(3) + 3 \)
     • \( 6 > 39 + 3 \)
     • \( 6 > 42 \) (False)

4. Point (2, 2):

   • For \( y < 12x \):
     • \( 2 < 12(2) \)
     • \( 2 < 24 \) (True)
   • For \( y > 13x + 3 \):
     • \( 2 > 13(2) + 3 \)
     • \( 2 > 26 + 3 \)
     • \( 2 > 29 \) (False)

None of the given points satisfy both inequalities simultaneously. If you are looking for a solution that fits both, a point would need to lie in the region defined by the intersection of the two inequalities. If you have any error or additional points to check, please provide that information!