Question

The sum of a two-digit number and the number formed by reversing the digits is 33. Also the sum of the digits is 4.Represent the above situation algebraically and graphically.

Answer 1

Step1: Algebraic representation.

Let the two digit number be $10x+y$

The number formed by reversing the digits $=10y+x$

Using first condition,

$$\begin{gathered} \left(10x+y\right)+\left(10y+x\right)=33 \\ \Rightarrow 11x+11y=33 \\ \Rightarrow x+y=3..........\left(1\right) \end{gathered}$$

Given that sum of digits $=4$

That is $x+y=4$ ……………….(2)

Pair of equations (1) and (2) represents the given situation algebraically

step2: Graphical representation

Find the points corresponding to $x+y=3$

$$\begin{gathered} x+y=3 \\ y=3-x \end{gathered}$$

Substituting different values for $x$ to get the values for $y$ as follows

$x$	0	1	3
$y$	3	2	0

Find the points corresponding to $x+y=4$

$$\begin{gathered} x+y=4 \\ y=4-x \end{gathered}$$

Putting different values on $x$, we get different values of $y$ as follows

$x$	0	2	4
$y$	4	2	0

plotting the points on a graph ,we get graphical representation of the situation as given below.