Question

Age of $X$ exceeds the age of $Y$ by \[7\] yrs. This statement can be expressed as linear equation as :
A. $X + Y + 7 = 0$\[7\]
B. $X - Y + 7 = 0$
C. $X - Y - 7 = 0$
D. $X + Y - 7 = 0$

Answer 1

Hint- In order to form a linear equation, we will first understand how to generally make a linear equation, then we will try to make a linear equation by using the given statement as $X$is greater than $Y$.

Complete step-by-step answer:
The age of $X$ exceeds the age of $Y$ by \[7\] years.
Linear equations are those of first order equations. In the coordinate system, those equations are specified for lines.
Linear equations are therefore equations of first degree, as they have the largest exponent of variables as $1$.
So the general formula for linear writing equation is \[Ax{\text{ }} + {\text{ }}By{\text{ }} + {\text{ }}C{\text{ }} = {\text{ }}0\]
Where $X$ and $Y$ are variable, and where \[A,{\text{ }}B\] and $C$ are constant
Now, as mentioned, it is obvious that $X$ is higher than $Y$
So then \[X > Y\]
It means we will add a few years with $Y$ to make both $X$and $Y$ equal
Then the equation is as
\[\begin{array}{*{20}{l}}
  {For{\text{ X }} = {\text{ Y }} + {\text{ }}7} \\
  \; \\
  {Or{\text{ X }} - {\text{ Y }} = {\text{ }}7} \\
  \; \\
  {Or{\text{ }}X - {\text{ Y }} - {\text{ }}7{\text{ }} = {\text{ }}0}
\end{array}\]

Hence choice C is the correct one.

Note- A linear equation in mathematics is an equation that can be put in the form where the variables are, and the coefficients, which are also real numbers. The coefficients can be considered as equation parameters, and can be arbitrary expressions, provided that they do not contain any of the variables.