Question

4. Which of the following points is asolution of y ≤ 5x – 1?A. (0, 2)B. (-3,0)C. (-1,-5)D. (2, 11)E. (7,2)

Answer 1

Solution

- The question tells us to find which of the points in the options is a solution to the following inequality:

$y\le5x-17$

- In order to find which point is a solution to the inequality, we can simply substitute the points into the inequality and see which one gives a true mathematical statement

- This is done below:

$\begin{gathered} y\le5x-17 \\ \\ \text{OPTION A:} \\ \mleft(0,2\mright)=\mleft(x,y\mright) \\ 2\le5(0)-17 \\ 2\le-17 \\ \text{THIS IS A FALSE MATHEMATICAL STATEMENT} \\ \\ \text{OPTION B:} \\ (-3,0)=(x,y) \\ 0\le5(-3)-17 \\ 0\le-35 \\ \text{THIS IS A FALSE MATHEMATICAL STATEMENT} \\ \\ \text{OPTION C:} \\ (-1,-5)=(x,y) \\ -5\le5(-1)-17 \\ -5\le-5-17 \\ -5\le-22 \\ \text{THIS IS A FALSE MATHEMATICAL STATEMENT} \\ \\ \text{OPTION D:} \\ (2,11)=(x,y) \\ 11\le5(2)-17 \\ 11\le10-17 \\ 11\le-7 \\ \text{THIS IS A FALSE MATHEMATICAL STATEMENT} \\ \\ \text{OPTION E:} \\ (7,2)=(x,y) \\ 2\le5(7)-17 \\ 2\le35-17 \\ 2\le18 \\ \text{THIS IS A TRUE MATHEMATICAL STATEMENT.} \end{gathered}$

Final Answer

The answer is (7, 2) (OPTION E)