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Questions and Answers
What is the solution of the system by substitution: 2x + y = -11, 3x - 4y = 11?
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?
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?
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?
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?
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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Description
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.
