Solving a system algebraically does not always provide a unique solution. Sometimes you get infinitely many solutions. Sometimes you get no solutions.
What are the solutions of the following systems? Explain.
How are the two equations in this system related?
Multiplying both sides of the first equation by
Elimination gives an equation that is always true. The two equations in the system represent the same line. This is a dependent system with infinitely many solutions.
Elimination gives an equation that is always false. The two equations in the system represent parallel lines. This is an inconsistent system. It has no solutions.
Solve each system by substitution.
Solve each system by elimination.