Algebra / Systems Linear Equations
Systems of Linear Equations
Parameter questions for systems of linear equations often involve one solution, no solution, infinitely many solutions, or a specified coordinate in the solution.
Least you need to know
- Equivalent equations represent the same line and give infinitely many solutions.
- Parallel distinct lines give no solution.
- A specified solution coordinate can be substituted into both equations.
Key notation
- $\begin{cases} ax+by=c \ dx+ey=f \end{cases}$ — A system of two linear equations
Worked example
- Compare multiples of the two equations or substitute a specified coordinate.
- Solve for the parameter that makes the condition true.
Common mistakes
- For infinitely many solutions, every term must be multiplied by the same factor.
How to recognize it
- The problem asks for a parameter that changes the number of solutions or a solution coordinate.
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