Systems of Equations
A system of linear equations is a set of two or more linear equations with the same variables. The solution to the system is the set of values that satisfies all equations simultaneously.
Methods of Solving
There are three primary methods to solve systems of linear equations:
- Graphing: Plotting lines to find the point of intersection.
- Substitution: Solving one equation for a variable and substituting it into the other.
- Elimination (Addition/Subtraction): Adding or subtracting equations to eliminate a variable.
Types of Solutions
- Consistent & Independent: One unique solution (lines intersect at one point).
- Consistent & Dependent: Infinitely many solutions (lines are identical).
- Inconsistent: No solution (lines are parallel).
Solved Problems
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