Question

Solve the equation 2x+1=x-3, and represent the solution on (i) the number line (ii) the Cartesian plane.

Answer 1

Hint: Start by finding the solution of the equation given in the question. Then represent the point on the number line and the line on the Cartesian plane.

Complete step-by-step answer:
Before starting with the solution, let us discuss the significance of linear equations. Linear equations represent the equation of a line on the Cartesian. The solution to two linear equations represents the meeting point of the two lines represented by the equations.
Now we will move to the solution to the given question. First, let us begin with the equation x-y=0.
2x+1=x-3
$\Rightarrow 2x-x=-3-1$
$\Rightarrow x=-4$
Now we will represent the solution on the number line.

Now we will represent the solution on the Cartesian plane. The equation x=-4 represents a line that is parallel to the y-axis when we represent it on the Cartesian plane.

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. 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.