Question

Find the solution of the pair of equations y = 0 and y = -6.

Answer 1

Hint: Given two equations of lines, we will find the solution of a pair of equations at the point of intersection of the two lines. Also, we will keep in mind the property that parallel lines never intersect each other.

Complete step-by-step answer:
We have been given two equations in the question as y = 0 and y = -6. We know that these are the equations of lines. So, first let us plot a graph corresponding to the equations given. So, the graph will look as follows.

Now, from the figure we can see that, the equation, y = 0 corresponds to the x-axis and the equation, y = -6, corresponds to a line which is parallel to the x-axis. Hence, we can see that both the lines are parallel lines and even if we extend any of these lines forward or backwards, there is no possibility that these two lines will ever intersect. But we know that the solution of the pair of lines is defined at the point of intersection of the two lines.
Since the lines do not intersect, these pair of equations have no solution.
Hence, there exist no solution for the lines, y = 0 and y = -6.

Note: The students must always remember that the equation of x-axis is y = 0 and the equation of y-axis is x = 0. And that, linear equations involving single variables, ‘y’ corresponds to a line parallel to the x-axis, similarly, linear equations involving single variables, ‘x’ corresponds to a line parallel to the y-axis. Most of the students may make a mistake thinking y = 0 represents the y-axis, and this leads to getting the wrong answer, so this must be avoided.