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Not every system of linear equations has a single solution. It is also possible for a linear solution to have no solution or an infinite number of solutions.
Lines with different slopes have one point of intersection. This type of system has one solution.
Lines with equal slopes and different \(y\)-intercepts are parallel and do not intersect. This type of system has no solution.
Lines with equal slopes and equal \(y\)-intercepts are coincident lines and have an infinite number of points of intersection. This type of system has an infinite number of solutions.
Some systems of equations include non-linear equations. The following investigation looks into some systems that involve non-linear equations. Use your understanding of systems of linear equations to help you through the investigation.