A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.
An independent system has one solution.
The solution to a system on linear equations in nunknown variables are ordered n-tuples such that their values satisfy each of the equations in the system. There need not be a solution or there can be more than one solutions.
there is no linear equations that has no solution every problem has a solution
A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
This is the case when there is only one set of values for each of the variables that satisfies the system of linear equations. It requires the matrix of coefficients. A to be invertible. If the system of equations is y = Ax then the unique solution is x = A-1y.
a system of equations
A system of linear equations.
It is a system of linear equations which does not have a solution.
Simultaneous equations have at least two unknown variables.
A system of linear equations that has at least one solution is called consistent.