Simultaneous Systems of Equations Solved Graphically

Solving simultaneous equations (systems of equations) by drawing graphs, and seeing where the two graphs meet (intersect). The coordinates of the point of intersection represent the solution of the equations. Notice that sometimes there are no solutions (the lines never meet because they are parallel), and sometimes there are inifinite solutions (the two lines are the same).

Author and programmer: Ron Barrow

UK Years 10-11, KS4, Higher GCSE Mathematics, Grades B - A* - Algebra and Graphs
US - Grade 10 Geometry

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Instructions below    See also: Simultaneous equations solved algebraically    Linear Equations ax + by = c

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How to Use this Applet

In this applet we are trying to investigate what we can learn about the coordinates of the point where two straight lines cross on a graph (if they do cross!).
We can vary Line 1 by changing values A, B and C. Similarly we can move Line 2 by varying D, E and F. Try it. As you vary the lines, notice what happens to the crossing point. Is there always a crossing point? Also, try to use algebra to check that you get the correct values for x and y when you solve Line 1 and Line 2 as simultaneous equations. The connection between the algebra and the geometry is a vital area of exploration. Enjoy yourself!