Systems of Equations and Inequalities Flashcards
Grade 10 · Math · Flashcards
Essential terms and concepts for solving systems of equations and inequalities.
Flashcards
- System of equations
- Two or more equations with the same variables solved simultaneously
- Solution to a system
- An ordered pair (x, y) that satisfies all equations in the system
- Graphing method
- Plot both equations; the intersection point is the solution
- Substitution method
- Solve one equation for a variable, then substitute into the other
- Elimination method
- Add or subtract equations to eliminate one variable, then solve
- Consistent system
- A system that has at least one solution
- Inconsistent system
- A system with no solution; lines are parallel
- Independent system
- A consistent system with exactly one solution; lines intersect once
- Dependent system
- A consistent system with infinitely many solutions; same line
- Linear inequality graph
- A half-plane; the boundary line is solid (≤,≥) or dashed (<,>)
- Feasible region
- The overlapping area satisfying all inequalities in a system
- Linear programming
- Optimizing a value (max/min) subject to a system of inequality constraints
- What does 0 = 5 mean when solving a system?
- No solution — the system is inconsistent
- What does 0 = 0 mean when solving a system?
- Infinitely many solutions — the system is dependent
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