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

(2,2)
left parenthesis 2 comma 2 right parenthesis

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

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

(10,5)

Answer 1

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

1. 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

2. 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

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 (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

Since none of the points satisfy both inequalities, it seems there is no solution among the given options.