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There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.
simultaneous equations
It is a set of equations, which is also called a system of equations. There may be no solution, a single (unique) solution or more than one - including infinitely many.
You don't need ANY factor. To find a unique solution, or a few, you would usually need to have as many equations as you have variables.
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There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.
simultaneous equations
A single equation is several unknowns will rarely have a unique solution. A system of n equations in n unknown variables may have a unique solution.
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.
Roughly speaking, to get a unique solution - or at least, a limited number of solutions - if you have 3 variables, you need 3 equations, not just 2. With the two equations, you can get a relationship between the three variables, but not a unique value for a, b, and c. To get the general relationship, solve both equations for "c", replace one in the other, and solve the resulting equation for "a" to get the relationship between the variables "a" and "b". Then, for any valid combination of values for "a" and "b", use the simpler of the original equations (a + b + c = 24) to get the corresponding value for "c".
It is a set of equations, which is also called a system of equations. There may be no solution, a single (unique) solution or more than one - including infinitely many.
Because this equation has four variables, it would require four unique equations involving only these four variables to solve.
You don't need ANY factor. To find a unique solution, or a few, you would usually need to have as many equations as you have variables.
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You can have any number of free variables. If you have m variables and n linear equations then, if m > n, you will have at least (m - n) free variables.
Cramer's rule is applied to obtain the solution when a system of n linear equations in n variables has a unique solution.