Algebra / Systems Linear Equations
Systems of Linear Equations
A system of two linear equations in two variables asks for values of both variables that make both equations true. Common methods include substitution, elimination, comparing equivalent equations, and interpreting the graphs as lines.
Least you need to know
- A solution to a system is an ordered pair that satisfies every equation.
- Parallel distinct lines give no solution, while identical lines give infinitely many solutions.
Key notation
- $(x,y)$ — The ordered pair that may solve both equations in a system
Worked example
- Add or subtract equations to eliminate one variable.
- Substitute back to find the other variable.
Common mistakes
- An ordered pair must satisfy both equations.
- Equivalent equations represent the same line.
How to recognize it
- The problem gives two equations with two variables.
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