How to Convert Equations with Variables?

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SUMMARY

The discussion focuses on converting equations with variables, specifically the equations 4/x - 3/y = 0 and 6/x + 3/2y = 2. The user introduces variables U = 4/x and V = 3/y to simplify the equations. A key point of confusion arises regarding the conversion of terms, particularly 6/x and 3/2y, where the correct transformation is established as 6/x = 1.5U and 3/2y = 0.5V. Precision in mathematical notation is emphasized to avoid misunderstandings.

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  • Understanding of algebraic equations and variable substitution
  • Familiarity with mathematical notation and precision
  • Basic knowledge of fractions and their manipulation
  • Ability to interpret and rewrite equations
NEXT STEPS
  • Practice variable substitution in algebraic equations
  • Learn about the implications of precision in mathematical expressions
  • Explore advanced algebra techniques for equation manipulation
  • Review common mistakes in interpreting mathematical notation
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Students learning algebra, educators teaching equation manipulation, and anyone seeking to improve their mathematical precision and clarity in variable usage.

smashbrohamme
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Homework Statement


4/x - 3/y=0
6/x +3/2y = 2


so I can make my own variables up.

U= 4/x
V= 3/y

my problem is, how do I convert that on the second equation

would 6/x turn into 1.5U and 3/2y turn into 1/V?
 
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smashbrohamme said:
would 6/x turn into 1.5U and 3/2y turn into 1/V?
No,
[tex]\frac{3}{2y} = 0.5V[/tex]

Or do you mean
[tex]\frac{3}{2}y[/tex]
?

You need to be precise!
 
no i mean 3/2y meaning, the 2 and the y will be multiplied.
 

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