High School What Does 'Simultaneous' Mean in Linear Equations?

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In the context of linear equations, "simultaneous" refers to multiple equations that must be solved together, meaning they share the same solution for the variables involved. For example, in the equations 2x + y = 4 and x - 2y = -3, the same values of x and y must satisfy both equations simultaneously. This concept is crucial for finding a unique solution that works for all equations in the system. Understanding simultaneous equations is fundamental in linear algebra and various applications in mathematics and engineering. The term emphasizes the interdependence of the equations in determining the solution.
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The term simultaneous in simultaneous linear equations does not make sense to me? Would you explain the what simultaneous mean there?

Example: "We have all solved simultaneous linear equations - for example,

2x + y = 4
x - 2y = -3 "

Source: Linear Algebra by Fraleigh/Beauregard.

Thank you.
 
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mech-eng said:
The term simultaneous in simultaneous linear equations does not make sense to me? Would you explain the what simultaneous mean there?

Example: "We have all solved simultaneous linear equations - for example,

2x + y = 4
x - 2y = -3 "

Source: Linear Algebra by Fraleigh/Beauregard.

Thank you.

It means more than one equation that must be satisfied by the same solution: in this case, the same values of ##x## and ##y## must satisfy both equations.

http://www.mathcentre.ac.uk/resources/Engineering maths first aid kit/latexsource and diagrams/2_13.pdf
 

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