Question

Which of the following points satisfies the linear inequality below? Select all correct answers.5x + 2y > 6Select all that apply:(0,5)(3, 1)(3, -4)(-4,1)

Answer 1

Given:

The inequality is given as 5x + 2y > 6.

The objective is to select all the correct options satisfying the inequality.

Step-by-step explanation:

Consider the point (x,y) = (0,5) and substitute in the given inequality.

`\begin{gathered} 5(0)+2(5)>6 \\ 0+10>6 \\ 10>6 \end{gathered}`

Thus, the point satisfies the inequality.

Consider the point (x,y) = (3,1) and substitute in the given inequality.

`\begin{gathered} 5(3)+2(1)>6 \\ 15+2>6 \\ 17>6 \end{gathered}`

Thus, the point satisfies the inequality.

Consider the point (x,y) = (3,-4) and substitute in the given inequality.

`\begin{gathered} 5(3)+2(-4)>6 \\ 15-8>6 \\ 7>6 \end{gathered}`

Thus, the point satisfies the inequality.

Now, consider the point (x,y) = (-4,1) and substitute in the given inequality.

`\begin{gathered} 5(-4)+2(1)>6 \\ -20+2>6 \\ -18>6 \end{gathered}`

Thus, the point does not satisfy the inequality.

Hence, options (1), (2), and (3) are the correct answer.