explain how to solve by graphing and why this works to find the solution for an equation.

Answer 1

To answer your question, we must first understand the relationship between an equation and a graph.

Let's assume a 2 variable equation y = x + 1

This equation is only true for some points on the X-Y graph.

For e.g., It is true for x=1 and y=2. But it is not true for x=1 and y=3.

So, the point corresponding x=1 and y=2 lies on the graph of this equation.

So, every 2 variable equation will have a graph which can be plotted on the X-Y coordinate system. Every point on this graph is a point that satisfies that equation.

Now coming to your question, some times we see questions in Equations where we are given two equations and asked for the solutions of X and Y. The question is basically asking you for points which lie on graphs of both of these equations. One way to solve these questions is to use the algebra methods to solve two equations with two variables by eliminating one of the variable. (I assume you are aware of this method).

The second method to solve these questions is to plot a graph for both of these equations and see the points where these two graphs intersect. The graph method can be cumbersome to find the exact solutions. But it can be very helpful to find out which quadrant the solutions lie in.