No. Here is a simple example where this is not the case:
x + y = 0
x + y = 1
If you subtract the first equation from the second, you get 0 = 1, which is clearly impossible. Graphically, you get two parallel lines, which never cross.
A system of linear equations that has at least one solution is called consistent.
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.
At least two - otherwise you have just one equation, not a system.
You have two unknown variables, x and y. You therefore need at least two independent equations to find a solution.
It means that at least one of the equations can be expressed as a linear combination of some of the other equations. A linear combination of equations is the addition (or subtraction) of equations. And since an equation can be added several times, it includes multiples of equations. For example, if you have x + 2y = 3 and 2x + y = 4 Then adding 2 times the first and 3 times the second gives 8x + 7y = 18 This is, therefore, dependent on the other 2. If you have n unknown variables, there will be a unique solution if, and only if, you must have a set of n independent linear equations.
A system of linear equations that has at least one solution is called consistent.
a linear equation
A system of equations is two or more equations that share at least one variable. Once you have determined your equations, solve for one of the variables and substitute in that solution to the other equation.
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.
No.
The MATLAB backslash command () is used to efficiently solve linear systems of equations by performing matrix division. It calculates the solution to the system of equations by finding the least squares solution or the exact solution depending on the properties of the matrix. This command is particularly useful for solving large systems of linear equations in a fast and accurate manner.
Simultaneous equations have at least two unknown variables.
Two (2)
At least two - otherwise you have just one equation, not a system.
Find values for each of the unknown variables (or at least as many as is possible for the system) that satisfy all the equations.
You have two unknown variables, x and y. You therefore need at least two independent equations to find a solution.
Due to non linear nature of the power flow equations, there are at least two solutions to every solvable power flow problem. The trivial one is zero voltage everywhere. There are also multiple solutions possible, for every capacitor bank (in service, out of service), every transformer with load taps. Iterative methods are ideal for solving power flow equations starting with answerer to the equations that are close to a correct solution.