Question

Linear inequalities often model the limits of real world variables. Suppose the difference between two numbers must be greater than 8. The inequality x - y > 8 can be used to represent the difference between these two unique numbers so that their difference is exceeds 8. X = a real number Y = a real number Use the inequality to verify each of the given coordinates (x, y) will satisfy this condition. (7,4),(3.8, 3) and (0,9).

Answer 1

The given inequality is

`x-y>8`

The given coordinates are (7,4), (3.8, 4) and (0,9).

Let's evaluate each coordinated pair in the inequality to see which one satisfies it.

For (7,4).

`\begin{gathered} 7-4>8 \\ 3>8 \end{gathered}`

Since 3 is not more than 8, we say (7,4) is not a solution.

For (3.8, 4).

`\begin{gathered} 3.8-4>8 \\ -0.2>8 \end{gathered}`

Since -0.2 is not more than 8, we say (3.8, 4) is not a solution.

For (0,9).

`\begin{gathered} 0-9>8 \\ -9>8 \end{gathered}`

Since -9 is not more than 8, we say (0,9) is not a solution.

Therefore, neither given point is a solution of the given inequality.