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Linear System

Jul 18, 2024

math

A linear system is a collection of multiple Linear Equations with the same variables. Finding the solution to a linear system involves finding the right variables, such that all equations are satisfied.

Examples

{3x+2yz=12x2y+4z=2x+12yz=0{\displaystyle {\begin{cases}3x+2y-z=1\\2x-2y+4z=-2\\-x+{\frac {1}{2}}y-z=0\end{cases}}} With the solution being: (x,y,z)=(1,2,2){\displaystyle (x,y,z)=(1,-2,-2)}

If you plot all of the equations, the solution lies in the intersection of their lines / planes. It could be a single number or an entire set. If there isn’t a common point across all of them – then there are no solutions.

400

{xy=13x+y=9{\displaystyle {\begin{cases}x-y=1\\3x+y=9\end{cases}}} With the solution being: (x,y)=(2,3){\displaystyle (x,y)=(2,3)}

400

References

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Commit c0daef5, deployed on Oct 01, 2024.