Question

Which points are solutions to the system of inequalities shown below? Check all that apply. < 2x 48 A. (3,3) B. (4,-2) C. (1,-4) D. (5,9) E. (5,3) F. (60)

Answer 1

`\begin{gathered} y<2x \\ y<8 \\ x>2 \end{gathered}`

Let's check every pair of points:

For:

`\begin{gathered} (3,3) \\ 3<8 \\ True \\ 3>2 \\ True \\ 3<2(3)=6 \\ True \end{gathered}`

Therefore, this point is a solution to the system of inequalities.

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For:

`\begin{gathered} (4,-2) \\ -2<8 \\ True \\ 4>2 \\ True \\ -2<2(4)=8 \\ True \end{gathered}`

Therefore, this point is a solution to the system of inequalities.

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For:

`\begin{gathered} (1,-4) \\ -4<8 \\ True \\ 1>2 \\ False \end{gathered}`

Therefore, this point is not a solution to the system of inequalities.

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For:

`\begin{gathered} (5,9) \\ 9<8 \\ False \end{gathered}`

Therefore, this point is not a solution to the system of inequalities.

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For:

`\begin{gathered} (5,3) \\ 3<8 \\ True \\ 5>2 \\ True \\ 3<2(5)=10 \\ True \end{gathered}`

Therefore, this point is a solution to the system of inequalities.

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For:

`\begin{gathered} (6,0) \\ 0<8 \\ True \\ 6>2 \\ True \\ 0<2(6)=12 \\ True \end{gathered}`

Therefore, this point is a solution to the system of inequalities.

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Hence, the correct answers are: