## Solving Lesson 8 Page 8 Math Workbook 10 – Kite>

Topic

Let x and y be two real numbers that differ from -1. Which of the following conclusions is correct?

A. $$x + y + xy \ne – 1$$

B. $$x + y + xy = – 1$$

C. $$x + y \ne – 2$$

D. $$xy \ne – 1$$

Solution method – See details

Check each clause. Type the answer by giving an example.

Detailed explanation

We have: $$x \ne – 1 \Rightarrow x + 1 \ne 0$$.

Similarly $$y + 1 \ne 0$$. Therefore: $$(x + 1)(y + 1) \ne 0$$ or $$x + y + xy \ne – 1$$

Choose A.

C is wrong, for example $$x = 0,y = – 2$$ satisfies but $$x + y = – 2$$

D is false, for example $$x = \frac{1}{2},y = – 2$$ satisfies but $$xy = – 1$$