Systems of Linear Equations - Graphical Approach
This large window java applet helps you explore the solutions of 2 by 2
systems of linear equations of the form
a1x + b1y = c1
a2x + b2y = c2.
A graphical approach is taken here in order to give a complete picture on solving systems of equations with the existing algebraic methods (elimination, cramer's rule,...). Also included in this site, a tutorial on solving systems of linear using analytical methods.
Interactive Tutorial Using Java Applet
What is the relationship between the geometric positions of the
lines representing the two equations of a system and the solutions
of the system ?
Use the scrollbar to set the constants a1, a2, b1, b2, c1 and c2 so
that the two lines have a point of intersection (x , y ). Check that the ordered pair (x , y), is the solution to the system (find a solution by any method you wish : substitution, elimination, cramer's rule,...) and compare.
Set a1, a2, b1 and b2 to values such that a1*b2 - a2*b1 = 0. How are
the two lines positioned with respect to each other ? How many solutions
the system has ? If (the determinant) a1*b2 - a2*b1 = 0, what is the relationship between the slopes of the two lines (are they equal for example?) ?
Set all 6 constants to values such that a1/a2 = b1/b2 = c1/c2. How
many solutions the system has ?Explain.
More references to systems of linear equations.