Types of solutions for a system of linear equations
1.) no solution2.) exactly one solution3.) infinitely many solutions
There are three types of solutions for a system of linear equations:
1. Unique Solution: A system of linear equations has a unique solution when there is only one set of values that satisfies all the equations in the system. Graphically, the unique solution represents the intersection point of two lines in a 2D plane or the intersection point of three planes in a 3D space.
2. No Solution: A system of linear equations has no solution when there is no set of values that satisfies all the equations in the system. Graphically, the no solution case represents two parallel lines in a 2D plane or three planes that do not intersect in a 3D space.
3. Infinitely Many Solutions: A system of linear equations has infinitely many solutions when there are multiple sets of values that satisfy all the equations in the system. Graphically, the infinitely many solutions case represents two identical lines in a 2D plane or three planes that intersect in a line in a 3D space.
The type of solution for a system of linear equations can be determined by either solving the equations algebraically or graphically, depending on the number of variables and equations involved.
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