High School Solutions to systems of equations

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SUMMARY

The discussion focuses on solving systems of equations represented by the formulas $$A = a_1 x + a_2 y$$ and $$B = b_1 x + b_2 y$$. It establishes that if the variables ##x## and ##y## are known while ##A## and ##B## remain unknown, the system is classified as undetermined, potentially yielding no solution or infinite solutions. The parameters ##a_1, a_2, b_1, b_2## are treated as unknowns, which complicates the determination of ##A## and ##B##, as they depend on these parameters.

PREREQUISITES
  • Understanding of linear equations and systems of equations
  • Familiarity with the concepts of dependent and independent variables
  • Knowledge of the terms "undetermined system" and "unique solutions"
  • Basic algebraic manipulation skills
NEXT STEPS
  • Explore methods for solving linear systems, such as substitution and elimination
  • Learn about the conditions for unique, infinite, and no solutions in systems of equations
  • Study the implications of parameter dependency in linear equations
  • Investigate graphical methods for visualizing solutions to systems of equations
USEFUL FOR

Students, educators, and professionals in mathematics or engineering fields who are interested in understanding the complexities of solving systems of equations and their implications in various applications.

kent davidge
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The set of equations $$A = a_1 x + a_2y$$ ¨$$B = b_1 x + b_2 y$$ can be solved for the unkowns ##x## and ##y##. Does it make sense to have ##x## and ##y## be known and instead ##A## and ##B## unkown?
 
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That is called a straightforward calculation
 
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kent davidge said:
Does it make sense to have ##x## and ##y## be known and instead ##A## and ##B## unknown?

What would ##a_1, a_2,b_1,b_2## be? Known or unknown?
 
Stephen Tashi said:
What would ##a_1, a_2,b_1,b_2## be? Known or unknown?
Sorry for not clarifying, I was regarding them as unkowns. Otherwise the solution would be obvious as @BvU pointed out.

I figured out the answer to my question. In such case, the system would be undetermined. It has either no solution of infinite solutions.
 
A and B have a unique value each that depends on all the parameters on the right side. They are never undetermined.
 

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