Which of the following points shows a solution to the simultaneous inequalities y>12x+5 and y<−2x+1?(1 point)

Question

Responses

(−1.6,4.2)
left parenthesis negative 1.6 comma 4.2 right parenthesis

(−5,5)
left parenthesis negative 5 comma 5 right parenthesis

(4,8)
left parenthesis 4 comma 8 right parenthesis

(1,5.5)

Answer 1

To determine which of the given points satisfies the simultaneous inequalities \(y > 12x + 5\) and \(y < -2x + 1\), we will evaluate each point against both inequalities.

1. Point \((-1.6, 4.2)\):

   • Check against \(y > 12x + 5\): \[ 4.2 > 12(-1.6) + 5 \implies 4.2 > -19.2 + 5 \implies 4.2 > -14.2 \text{ (True)} \]
   • Check against \(y < -2x + 1\): \[ 4.2 < -2(-1.6) + 1 \implies 4.2 < 3.2 + 1 \implies 4.2 < 4.2 \text{ (False)} \]
   • Result: Not a solution.

2. Point \((-5, 5)\):

   • Check against \(y > 12x + 5\): \[ 5 > 12(-5) + 5 \implies 5 > -60 + 5 \implies 5 > -55 \text{ (True)} \]
   • Check against \(y < -2x + 1\): \[ 5 < -2(-5) + 1 \implies 5 < 10 + 1 \implies 5 < 11 \text{ (True)} \]
   • Result: This point is a solution.

3. Point \((4, 8)\):

   • Check against \(y > 12x + 5\): \[ 8 > 12(4) + 5 \implies 8 > 48 + 5 \implies 8 > 53 \text{ (False)} \]
   • Result: Not a solution.

4. Point \((1, 5.5)\):

   • Check against \(y > 12x + 5\): \[ 5.5 > 12(1) + 5 \implies 5.5 > 12 + 5 \implies 5.5 > 17 \text{ (False)} \]
   • Result: Not a solution.

Based on the evaluations, the only point that satisfies both inequalities is \((-5, 5)\).