Find the solutions of simultaneous equations

Basic idea: Consider intersections of the graphs of the functions and in xb plane.

First, draw the graph of the function . Since, it is rational function(where its asymptotes are b-axis and b=-x). Here is the graph.

Next, add the graph of the function .
Since b=-2x, it is the linear function passing the origin and with the slope -2.

 As you can see, the graph of meets the graph of at two points whose x-coordinators are -1 and 1, respectively. That is, the solutions of these equations are -1 and 1.

Now, solve the equations in a algebraic way.

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