Question

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

Answer 1

Hint: Let the unknown costs of the notebook and the pen be x and y, respectively. After that use the relation between the cost of the notebook and the cost of the pen to get an equation in terms of x and y.

Complete step-by-step answer:

Before starting with the solution, let us discuss the significance of linear equations in two variables. Linear equations in two variables represent the equation of a line on the Cartesian plane.

Now we will move to the solution to the given question. First, we will let the price of the notebook be Rs. x and the cost of the pen be Rs. y.

According to the statement given in the question, the cost of the notebook is twice the cost of the pen. This can be mathematically represented as:

x=2y

Now, as this is a linear equation, it represents a line. In order to represent this in a Cartesian plane, we convert the equation of line to the slope form. On doing so, we get

x=2y

\[\Rightarrow y=\dfrac{1}{2}x\]

Therefore, the slope of the line is half. This can be geometrically represented as:

Note: Be careful with the signs and calculations as in such questions, the possibility of making a mistake is either of the sign or a calculation error. Also, we should be clear that a solution can represent different geometries when represented in planes with different dimensions, and all the points lying on these geometries would represent a solution to the linear equation. For example: when the solution of the above equation is represented on a number line, i.e., a single dimensioned plane, the geometry formed is just a point while on the Cartesian plane, it is represented by a straight line. Further, if we extend it to a 3-D plane, we will find the same solution will represent a plane.