Question

Age of \[x\] is more than the age of \[y\] by 10 years. Express this statement in linear equations.

Answer 1

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.

Complete step-by-step answer:
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 \[\left( {{\text{x}} - {\text{y }} = 10} \right)\].