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Question

Which point is a solution for the simultaneous inequalities:

y≤4x−5


y<2x−7


(1 point)
Responses

(7, 12)
(7, 12)

(5, 3)
(5, 3)

(0,15)
(0,15)

(15,0)
(15,0)

Answer 1

To determine which point is a solution for the given simultaneous inequalities \(y \leq 4x - 5\) and \(y < 2x - 7\), we need to check each point against both inequalities.

1. (7, 12):

   • For \(y \leq 4x - 5\):
     • \(12 \leq 4(7) - 5 \Rightarrow 12 \leq 28 - 5 \Rightarrow 12 \leq 23\) (True)
   • For \(y < 2x - 7\):
     • \(12 < 2(7) - 7 \Rightarrow 12 < 14 - 7 \Rightarrow 12 < 7\) (False)

2. (5, 3):

   • For \(y \leq 4x - 5\):
     • \(3 \leq 4(5) - 5 \Rightarrow 3 \leq 20 - 5 \Rightarrow 3 \leq 15\) (True)
   • For \(y < 2x - 7\):
     • \(3 < 2(5) - 7 \Rightarrow 3 < 10 - 7 \Rightarrow 3 < 3\) (False)

3. (0, 15):

   • For \(y \leq 4x - 5\):
     • \(15 \leq 4(0) - 5 \Rightarrow 15 \leq 0 - 5 \Rightarrow 15 \leq -5\) (False)

4. (15, 0):

   • For \(y \leq 4x - 5\):
     • \(0 \leq 4(15) - 5 \Rightarrow 0 \leq 60 - 5 \Rightarrow 0 \leq 55\) (True)
   • For \(y < 2x - 7\):
     • \(0 < 2(15) - 7 \Rightarrow 0 < 30 - 7 \Rightarrow 0 < 23\) (True)

Based on the evaluations, the point (15, 0) satisfies both inequalities.

So the correct answer is:

(15, 0)