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there is no linear equations that has no solution every problem has a solution
A system of linear equations that has at least one solution is called consistent.
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.
simultaneous equations
Linear system