1. Introduction: Two Lines, One Meeting Point
You already know how to draw the graph of one equation like x + y = 5. It is a straight line, and every point on that line is an answer. (3, 2) works, (1, 4) works, (5, 0) works — there are endless answers. One equation in two unknowns can never pin down a single answer.
But real problems give you two facts at once. "Two notebooks and a pen cost ₹8. One notebook and a pen cost ₹5." That is two equations together — a pair of linear equations. And a pair usually has exactly one answer.
Stop scrolling. Try it in your head before reading on. If each equation is a straight line, and you draw both on the same graph, what single point belongs to both lines at once?
That shared point — where the two lines cross — is the answer that satisfies both equations together. The whole graphical method is just this: draw both lines, look at where they meet, read off the point. No formula-juggling, just looking.
By the end of this section you will be able to plot any two linear equations, find their meeting point, and say straight away whether a pair has one answer, no answer, or endlessly many — just from the picture.