Question

Decide whether the ordered pair is a solution of the inequality. $$y

Short answer

No, the ordered pair (1,1) is not a solution to the inequality.

Step-by-step solution

Substitute the values into the inequality

The ordered pair provided is (1,1). This should be substituted into the inequality, i.e., \(y<x^{2}-2 x-5\). Here x = 1 and y = 1. So the inequality becomes \(1<1^{2}-2*1-5\).

Solve the inequality

Having substituted the values, resolve the right side of the inequality. This is achieved by simplifying \(1^{2}-2*1-5\), which equals -4. Therefore, the inequality now reads \(1<-4\).

Decide if the inequality is true

Looking at the inequality \(1<-4\), it is clear that 1 is not less than -4. Thus, the inequality is false, meaning the ordered pair (1,1) is not a solution.