Chapter 5.6, Problem 4E

To determine

To determine whether the ordered pair $\left(5,2\right)$ is a solution of inequality:

  $x-y\le 0$

Answer to Problem 4E

No, $\left(5,2\right)$ is not a solution of the given inequality.

Explanation of Solution

Given:

  $x-y\le 0$

Concept Used:

To check whether the ordered pair $\left(a,b\right)$ is a solution of an inequality substitute a for x and b for y, and then check whether it make inequality true.

Calculation:

To determine whether the ordered pair $\left(5,2\right)$ is a solution of inequality:

  $x-y\le 0$

Substitute 5 for x and 2 for y, in given inequality, as

  $\begin{array}{c}5-2\le 0\\ \Rightarrow 2\le 0\end{array}$

But above is a contradiction(as 2 is neither less than 0 nor equals to 0). Thus, $\left(5,2\right)$ doesn’t satisfies the given inequality.

Thus, the ordered pair $\left(5,2\right)$ is not a solution of given inequality.