Questions and Answers
What is the solution of the system by substitution: 2x + y = -11, 3x - 4y = 11?
C.(-3,-5)
What is the solution of the system using elimination: 2x + 6y = -12, 5x - 5y = 10?
B.(0,-2)
What is the solution of the system: -3x - 2y = -12, 9x + 6y = -9?
B.No solutions
What is the solution of the system: x - y = 11, -x + y = -11?
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How many adults and children attended the ball game if there were 45 people in total and twice as many children as adults?
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Study Notes
Solving Systems of Equations
-
Substitution Method
- Problem: 2x + y = -11
- Problem: 3x - 4y = 11
- Solution: C. (-3, -5)
-
Elimination Method
- Problem: 2x + 6y = -12
- Problem: 5x - 5y = 10
- Solution: B. (0, -2)
-
No Solution Scenario
- System: -3x - 2y = -12
- System: 9x + 6y = -9
- Conclusion: B. No solutions (indicating parallel lines)
-
Infinitely Many Solutions
- System: x - y = 11
- System: -x + y = -11
- Conclusion: C. Infinitely many solutions (redundant equations)
-
Application Problem
- Context: Group of 45 people at a ballgame
- Condition: Twice as many children as adults
- System of equations formed:
- Let x = number of adults
- Let y = number of children
- Equations: x + y = 45, y = 2x
- Solution: A. 15 adults, 30 children
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Test your understanding of solving systems of equations algebraically with these quick check flashcards. Each card presents a unique system for you to solve using either substitution or elimination methods. Perfect for quick revision and understanding of algebraic concepts.
