How Do You Solve These Simultaneous Linear Equations for L and X?

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SUMMARY

The discussion focuses on solving simultaneous equations involving the variables L and X, specifically the equations 0.182(L² + X²) = 160² and 0.182[(555.56 + L)² + X²] = 240². Participants confirm that these equations are not linear due to the squared terms. The recommended approach is to solve the first equation for X² and substitute it into the second equation to isolate L. This method allows for a systematic resolution of the variables.

PREREQUISITES
  • Understanding of algebraic manipulation and substitution methods.
  • Familiarity with quadratic equations and their properties.
  • Basic knowledge of mathematical notation and operations.
  • Ability to solve equations involving squared terms.
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  • Explore the implications of non-linear equations in algebra.
  • Learn about graphing quadratic functions to visualize solutions.
  • Investigate numerical methods for solving simultaneous equations.
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Students studying algebra, educators teaching mathematical concepts, and anyone looking to improve their problem-solving skills in equations involving multiple variables.

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Homework Statement


Find value L and X.

0.182(L2+X2)=1602
0.182[(555.56+L)2+X2]=2402
 
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Technically, these aren't linear equations, are they, since both L and X are squared. You can solve this through substitution. I would solve the 1st equation for X2, then substitute the result into the 2nd equation and then solve for L. Try it, and let us know what you get.


69
 
but i still don't know why i can't solve it out ...can you show me how you do it? ^^
 
Well, what have you tried to do? Have you solved 0.18^2(L^2+ X^2)= 160^2? If so, what did you get?

What equation do you get when you replace X^2 by that in 0.182[(555.56+L)^2+X^2]=2402?
 

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