Question

Write a linear equation in two variables to represent the following statement.
The cost of a pen is thrice the cost of a pencil.
A.x=3y, where x= cost of a pen and y=cost of a pencil.
B. x=2y, where x=cost of a pen and y=cost of a pencil.
C.2x=3y, where x=cost of a pen and y=cost of a pencil.
D.x=y, where x=cost of a pen and y=cost of a pencil.

Answer 1

Hint: By assuming the variables for the cost of a pen and the cost of a pencil we can form the linear equation. Linear equation is the polynomial whose degree of polynomial is one i.e. the highest power of the terms will be one. E.g. $4y + 1 = 0,5x = 8z$etc.

Complete step-by-step answer:
If we want to represent the given statement in the linear equation form then we have to assume x as cost of a pen and y as cost of a pencil.
Now if we see option A then the linear equation is
$ \Leftrightarrow x = 3y$, where $x = $ cost of a pen and $y = $ cost of a pencil.
If we convert this into a statement form then it can be written as the cost price of a pen is thrice the cost of a pencil.
Now if we see option B than the linear equation is
$ \Leftrightarrow x = 2y$, where $x = $ cost of a pen and $y = $ cost of a pencil.
If we convert this into statement form then it can be written as the cost price of a pen is twice the cost of a pencil.
Now if we see option C than the linear equation is
$ \Leftrightarrow 2x = 3y$, where $x = $ cost of a pen and $y = $ cost of a pencil.
If we convert this into a statement form then it can be written as twice the cost price of a pen is thrice the cost of a pencil.
Now if we see option D than the linear equation is
$ \Leftrightarrow x = y$, where $x = $ cost of a pen and $y = $ cost of a pencil.
If we convert this into a statement form then it can be written as the cost price of a pen is equal to the cost of a pencil.
By comparing all the options with the statement given we found that option A is correct.
So, the correct option is A.

Note: Degree of a polynomial is defined as the highest power of the terms in a polynomial.
If we want to find if a polynomial is linear or not? Then first of all find the exponent of highest value and that exponent is called degree of polynomial. If the degree of polynomial is one then it is a linear equation.
If the degree of polynomial is two then it is quadratic polynomial.