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.
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.
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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.
No. At least, it can't have EXACTLY 3 solutions, if that's what you mean. A system of two linear equations in two variables can have:No solutionOne solutionAn infinite number of solutions