How do I solve systems of equations with multiple variables?

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To solve systems of equations with multiple variables, start by selecting one variable from one equation and solving for it. Substitute this expression into the other equation to find the value of the second variable. Once both variables are determined, you can verify the solution by plugging them back into the original equations. This method effectively utilizes substitution to simplify the problem. Understanding these steps is crucial for solving complex systems of equations.
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How do I solve this:
.5x+.5y=.5
.5x^2+.5y^2=1/3
 
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working with multiple equations to find an equal multiple of variables requires solving and subsitution.

First, pick x or y, and one equation, and solve the chosen equation for the chosen variable.

The term that x is equal to can be substituted in for x in the leftover equation to find a specific y, which can then be substituted into either equation to find x.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

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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