SOLUTION: How many solutions does a system of linear equations in three variables have?Can systems of linear equations have infinitely many solutions? Under what circumstances could that occ

Question 449034: How many solutions does a system of linear equations in three variables have?Can systems of linear equations have infinitely many solutions? Under what circumstances could that occur?
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

A system of linear equations means two or more linear equations. (In plain speak: 'two or more lines') If these two linear equations intersect, that point of intersection is called the solution to the system of linear equations.
Systems of equations that have three variables are systems of planes. Since all three variables equations such as describe a a three dimensional plane.
Like systems of linear equations, the solution of a system of planes can be , or .
If there is

at which

, the system of 3 variable equations has .
If the three planes , then the three variable system has point in common, and has solution.
If the three planes intersect and the three variable system has a of intersection,it will have an number of .

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