Questions and Answers
An inconsistent system of equations would be composed of intersecting lines.
False
A dependent system of equations would be composed of coincident lines.
True
A system of linear equations with no solutions would be described as an inconsistent system.
True
What is the term for the additional variable used to determine the values of the original variables in the ordered pair of a system of equations whose solution is an infinite number of solutions?
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What is the solution for the following system of equations? (7,1)
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Type the least common multiple of the x coefficients for the following system of equations: 3x-4y=20, 7x-13y=-15.
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Solve the system of equations: x+2y=7, 2x-5y=-4.
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Solve the system of equations: 2x+3y=7, 3x-2y=4.
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Study Notes
Systems of Equations
- An inconsistent system is characterized by parallel lines, indicating no solutions.
- A dependent system consists of coincident lines, meaning an infinite number of solutions exists.
- Systems of equations that lack solutions are termed inconsistent.
Parameters and Solutions
- The term parameter refers to an additional variable used in systems with infinite solutions to define the original variables.
- For the system of equations x + 2y = 7 and 2x - 5y = -4, the solution is the ordered pair (3, 2).
- The solution for the system 2x + 3y = 7 and 3x - 2y = 4 is the ordered pair (2, 1).
Least Common Multiple
- The least common multiple (LCM) of the x coefficients for the system of equations 3x - 4y = 20 and 7x - 13y = -15 is 21.
Key Equations
- The ordered pair (7, 1) is the solution for an unspecified system of equations provided in the original text.
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Description
Test your understanding of systems of equations, including concepts like inconsistent, dependent systems, parameters, and solutions. This quiz will challenge you to identify the characteristics and solutions related to various equations. Perfect for students looking to reinforce their knowledge in algebra!
