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Graphical solution - systems of equations

A graphical solution to a system of equations means that you draw the system of equations graphs and the reading of it, or the xx- and yy-values where the graphs intersect. Say you have the system of equations {2y=62xx=y1.\begin{cases}2y=6-2x \\ x=y-1. \end{cases} Thus, it should be to find the pair of xx and yy-values that solve the both of the equations at the same time. It is in defining the intersection.


Start with the writing of the equations kk-form by solve yy in the left side: {y=3xy=x+1.\begin{cases}y=3-x \\ y=x+1. \end{cases}

You can either draw the features by hand or with a graphing calculator.

Now you can read of the point of intersection.

The graphs intersect in the point (1,2).(1,2). The solution to the system of equations is therefore {x=1y=2.\begin{cases}x=1 \\ y=2. \end{cases}

Often it is practical to use calculator to make a graphic solution.