Question

# Age of $x$ is more than the age of $y$ by 10 years. Express this statement in linear equations.

Hint: Here first of all we should know the exact meaning of a linear equation that is defined as the equation between two variables that gives a straight line when shown graphically. We should also remember that at least a variable is required to convert any statement into a linear equation.

Let us take an example to understand this problem properly.
Now let us assume ‘p’ is older than ‘q’ and the age of ‘p’ is more than ‘q’ by 6 years.
This means that ‘p’ is 6 years older than ‘q’.
Let the age of ‘p’ is ‘a’ years and the age of ‘q’ is ‘b’ years.
So as we know that age of p is 6 years more than age of q. So we can say that
Age of p must be equal to age of q + 6.
So, ‘a’ must be equal to ‘b + 6’.
Now the linear equation for this will be
${\text{a }} = {\text{b}} + 6$ years
Similarly the given question says that the age of $x$ is more than the age of $y$.
It means that $\left( {{\text{x }} > {\text{y}}} \right)$
As $x$ is more than $y$ by 10 years
So the age of $x$ must be equal to age of $y$ with addition of 10 years which means that
${\text{x}} = {\text{y}} + 10$.
Hence the linear equation for this is ${\text{x}} = {\text{y}} + 10$.

NOTE:- Whenever we come up with this type of problem of forming a linear equation we should remember that the equation must be in format consisting of all the variables mentioned in the statement ( here it is given in two variables i.e. x and y ). There are others ways also to represent the following statement in linear equation i.e. the difference in ages of x and y must be equal to 10 because x is 10 years more than y so the statement hence formed will be $\left( {{\text{x}} - {\text{y }} = 10} \right)$.