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.
A consistent system with independent equations is one in which there is at least one solution, and the equations do not overlap in their constraints, meaning that no equation can be derived from another. In such a system, the equations represent different planes (or lines in two dimensions), and they intersect at one unique point (in the case of two variables) or along a line (for three variables). This unique intersection indicates that the system has a single solution that satisfies all equations simultaneously.
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.
A consistent system of equations is one in which there is at least one set of values for the variables that satisfies all the equations simultaneously. In graphical terms, this means that the lines or planes represented by the equations intersect at one or more points. A consistent system can be classified as either independent (with a unique solution) or dependent (with infinitely many solutions). In contrast, an inconsistent system has no solutions, meaning the equations represent parallel lines or planes that do not intersect.
At least two - otherwise you have just one equation, not a system.
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.
A consistent system of equations is one in which there is at least one set of values for the variables that satisfies all the equations simultaneously. In graphical terms, this means that the lines or planes represented by the equations intersect at one or more points. A consistent system can be classified as either independent (with a unique solution) or dependent (with infinitely many solutions). In contrast, an inconsistent system has no solutions, meaning the equations represent parallel lines or planes that do not intersect.
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.