Question

$10+y\ge 10$
$x-10\ge -10$

If the above inequalities hold good, then which of the following is true for any integers $x$ and $y$?

• A. $x\le 0,y\ge 0$
• B. $x\ge 0,y\ge 0$
• C. $x\ge 0,y\ge -20$
• D. $x\ge 0,y\le 0$

Answer 1

The correct option is B $x\ge 0,y\ge 0$

Given:

$\underset{–}{10+y\ge 10}---\left(1\right)$

To isolate $y,$ we subtract 10 from both sides of $\left(1\right).$

The sign of the inequality remains unchanged when we subtract the same number from both sides.

$⟹10+y-10\ge 10-10$

i.e., $y\ge 0$

$\underset{–}{x-10\ge -10}---\left(2\right)$

We add 10 to both sides of $\left(2\right)$ to isolate $x.$ Again, the sign of the inequality remains unchanged.

$\therefore x-10+10\ge -10+10$

i.e., $x\ge 0$

$\therefore x\ge 0,y\ge 0$