Question

How many ordered pairs are possible for the equation $2x+y=10$ for non-negative integers x and y.

Answer 1

We need to find the ordered pairs of non-negative integers $x$ and $y$ for the equation $2x+y=10.$

Let's substitute possible values of $x$ to obtain the corresponding values of $y.$

For $x=0,$
$\Rightarrow 2\left(0\right)+y=10$
$\Rightarrow y=10$

Similarly, by substituting $x=1,2,3,4,5$ of obtain non-negative integers of $y.$
$x$ $y$

0	1	2	3	4	5
10	8	6	4	2	0

$\therefore$ There are $10$ ordered pairs of $(x,y).$