Algebra 1
Systems of Linear Equations flashcards
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- What does intersection as solution mean?Graphing Systems
- A shared point of two graphed equations.
- Why substitute into both equations?Graphing Systems
- A point on only one line is not a system solution.
- How would you define one intersection?Graphing Systems
- A system with one common coordinate pair.
- What causes one solution for distinct lines?Graphing Systems
- Different slopes.
- What is meant by graph precision?Graphing Systems
- Using a graph as an estimate rather than automatic exact proof.
- Why verify an estimated intersection?Graphing Systems
- Drawing scale and thickness can hide exact values.
- What does isolating a variable mean?Substitution
- Replacing a variable with an equivalent expression.
- Why may substitution simplify a system?Substitution
- It reduces two variables to one equation.
- How would you define solving and back-substitution?Substitution
- Recovering a missing coordinate after substitution.
- Why is one coordinate not a complete system answer?Substitution
- A solution is an ordered pair.
- What is meant by checking both equations?Substitution
- Verification in all original system equations.
- Does satisfying one equation suffice?Substitution
- No, both must hold.
- What does adding equations mean?Elimination
- Combining equations to remove a variable.
- What must be aligned before addition?Elimination
- Coefficients of the same variables and constants.
- How would you define scaling before elimination?Elimination
- Preparing coefficients so one variable cancels.
- Why multiply every term of an equation?Elimination
- Partial scaling would change its solutions.
- What is meant by solution verification?Elimination
- Testing a pair after algebraic elimination.
- What does a failed check indicate?Elimination
- An arithmetic error or invalid candidate.
- What does parallel lines mean?Special Cases
- An inconsistent system of distinct parallel lines.
- What algebraic result signals no solution?Special Cases
- A contradiction such as 0=5.
- How would you define coincident lines?Special Cases
- A dependent system with infinitely many shared points.
- What algebraic result can signal this?Special Cases
- An identity such as 0=0.
- What is meant by classifying a system?Special Cases
- Classification by shared solution count.
- Why inspect both slope and intercept?Special Cases
- Equal slopes can describe parallel or identical lines.
- What does defining two variables mean?Systems in Context
- Two unknown quantities linked by simultaneous constraints.
- Why include units?Systems in Context
- It prevents confusing prices with item counts.
- How would you define writing independent constraints?Systems in Context
- Two conditions that an answer must satisfy simultaneously.
- Why check both constraints?Systems in Context
- A pair may fit one story detail but not the other.
- What is meant by feasible solutions?Systems in Context
- A mathematically and contextually permitted system solution.
- Can a negative count be accepted as a real-world answer?Systems in Context
- No, unless the problem explicitly gives another meaning.