Here are the essential concepts you must grasp in order to answer the question correctly.
System of Linear Equations
A system of linear equations consists of two or more linear equations involving the same set of variables. The solutions to the system are the values of the variables that satisfy all equations simultaneously. The system can have one solution, no solution, or infinitely many solutions, depending on the relationships between the equations.
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Conditions for No Solution
A system of linear equations has no solution when the lines represented by the equations are parallel, meaning they have the same slope but different y-intercepts. This occurs when the equations are inconsistent, indicating that there is no point at which the lines intersect.
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Conditions for Infinitely Many Solutions
A system of linear equations has infinitely many solutions when the equations represent the same line, meaning they are dependent. This occurs when one equation can be derived from the other through multiplication or addition, resulting in identical slopes and y-intercepts.
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