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Does the generic solution to a dependent system always have to be written in terms of
No, you can write the generic solution in terms of any of the variables, but it is common to write it in terms of x and if needed and
Solve the following system.
Infinite number of solutions of the form
Access these online resources for additional instruction and practice with systems of equations in three variables.
Can a linear system of three equations have exactly two solutions? Explain why or why not
No, there can be only one, zero, or infinitely many solutions.
If a given ordered triple solves the system of equations, is that solution unique? If so, explain why. If not, give an example where it is not unique.
If a given ordered triple does not solve the system of equations, is there no solution? If so, explain why. If not, give an example.
Not necessarily. There could be zero, one, or infinitely many solutions. For example, is not a solution to the system below, but that does not mean that it has no solution.
Using the method of addition, is there only one way to solve the system?
Can you explain whether there can be only one method to solve a linear system of equations? If yes, give an example of such a system of equations. If not, explain why not.
Every system of equations can be solved graphically, by substitution, and by addition. However, systems of three equations become very complex to solve graphically so other methods are usually preferable.
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