Systems of Linear Equations
Graphs the two lines associated with a system of two linear equations in
two variables, showing the solution of the system as the point where
the lines intersect (if a unique solution exists).
How to use
How to use
The text input fields can accept any decimal number input.
- Enter coefficients into the corresponding text input fields
(enter the value for coefficient A into the text input field
marked "A=", for B into the field
marked "B=", etc.).
the "Graph" button (this button can also be
used to refresh the graph)
- To reset the graph and all input fields to default values, click the
The buttons under the graph
allow various manipulations of
the graph coordinates.
The labels under the text input field tell whether the system is
independent, dependent, or inconsistent, and in the independent case
also give the coordinates of the solution point (where the two lines
cross). This information is determined as follows:
- If AE-DB=0, then the system is either dependent
or inconsistent. To determine these cases:
- If CE-FB=0, then the system is dependent.
In this case,
the two equations describe the same line, and all points on that line
are solutions of the system. The label will read:
"solutions: entire line".
- Otherwise, the system is inconsistent. In this case, the two
equations describe parallel lines, which never cross, so there is no
solution point. The label will read:
- Otherwise, the system is independent, and the two equations
describe nonparallel lines, which cross exactly once. The point
the two lines cross is the solution point for the system.
The coordinates of the point (x,y) are determined using
The label will display this solution point.