Question

1b. Check if each of these points is a solution to the inequality 2y - X> 1:*SolutionNot a solution(0,2)OO(8, 1/2)OO(-7-3)O

Answer 1

Given:

`2y-x>1`

To test the points that is a solution to the inequality;

`\begin{gathered} At\text{ (0,2)} \\ x=0,y=2 \\ \\ \text{Substituting into the inequality,} \\ 2y-x>1 \\ 2(2)-0 \\ 4 \\ \text{Since 4>1, then the point (0,2) satisfies the inequality and is a solution} \end{gathered}`

Therefore, (0,2) is a solution.

`\begin{gathered} At\text{ (8,}(1)/(2)\text{)} \\ x=8,y=(1)/(2) \\ \\ \text{Substituting into the inequality,} \\ 2y-x>1 \\ 2((1)/(2))-8 \\ 1-8 \\ -7 \\ \\ \text{Since -7< 1, then the point (8,}(1)/(2)\text{) does not satisfy the inequality and is not a solution} \end{gathered}`

Therefore, (8, 1/2) is not a solution.

`\begin{gathered} At\text{ (-7,-3)} \\ x=-7,y=-3 \\ \\ \text{Substituting into the inequality,} \\ 2y-x>1 \\ 2(-3)-(-7) \\ -6+7 \\ 1 \\ \\ \text{Since 1=1, then the point (-7,-3) does not satisfy the inequality and is not a solution} \end{gathered}`

Therefore, (-7,-3) is not a solution.

Also, the graph of the inequality is shown below with the given points.

It can be seen that only the point (0,2) falls within the region of the solution.

Therefore, the answer is summarized below;