It is essentially a list of equations that have common unknown variables in all of them. For example,
a+b-c=3
4a+b+c=1
a-2b-7c=-2
would be a system of equations. If there are the same number of equations and variables you can usually, but not always, find the solutions. Since there are 3 equations and 3 variables (a, b, and c) in this example one can usually find the value of those three variables.
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It is essentially a list of equations that have common unknown variables in all of them. For example,
a+b-c=3
4a+b+c=1
a-2b-7c=-2
would be a system of equations. If there are the same number of equations and variables you can usually, but not always, find the solutions. Since there are 3 equations and 3 variables (a, b, and c) in this example one can usually find the value of those three variables.
There are many types of equations such as straight line equations, simultaneous equations and quadratic equations.
The solution of a system of linear equations is a pair of values that make both of the equations true.
An inconsistent system of equations is when you have 2 or more equations, but it is not possible to satisfy all of them at the same time. (E.g if you have 3 equations, but can only satisfy 2 at once, it is an inconsistent system).
It probably means that one of the equations is a linear combination of the others/ To that extent, the system of equations is over-specified.
A system of equations will have no solutions if the line they represent are parallel. Remember that the solution of a system of equations is physically represented by the intersection point of the two lines. If the lines don't intersect (parallel) then there can be no solution.
An "inconsistent" set of equations. If they are all linear equations then the matrix of coefficients is singular.