How Do You Use Elimination to Solve Linear Systems with Three Variables?

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To solve the linear system using elimination, start by manipulating the equations to eliminate one variable at a time. Begin with the first two equations to eliminate one variable, then substitute the result into the third equation. Continue this process until all variables are solved. It's essential to show your work to facilitate understanding and receive further guidance. Engaging with similar examples in textbooks can also provide clarity on the elimination method.
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solve each given linear system by the method of elimination
2x-3y+4z=-12
x-2y+z=-5
3x+y+2z=1

How to solve this problem. What should I do first?
 
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Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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