Is There a Simpler Method to Solve Similar Linear and Quadratic Systems?

  • Context: High School 
  • Thread starter Thread starter azure kitsune
  • Start date Start date
  • Tags Tags
    System
Click For Summary
SUMMARY

The discussion centers on solving a system of equations represented as ax + by = c and ax² + by² = c, where a, b, and c are constants. The initial method involves isolating x in the first equation and substituting it into the second, leading to a quadratic equation in y that is solved using the quadratic formula. However, participants suggest that this method, while effective, may not be the simplest approach. The consensus leans towards the traditional substitution method as the most straightforward solution for this type of system.

PREREQUISITES
  • Understanding of linear equations and their forms
  • Familiarity with quadratic equations and the quadratic formula
  • Basic algebraic manipulation skills
  • Knowledge of substitution methods in solving equations
NEXT STEPS
  • Explore alternative methods for solving systems of equations, such as elimination
  • Study the implications of using graphical methods for visualizing solutions
  • Learn about the properties of linear and quadratic functions
  • Investigate numerical methods for approximating solutions to complex systems
USEFUL FOR

Students in mathematics or physics, educators teaching algebraic methods, and anyone interested in simplifying the process of solving systems of equations.

azure kitsune
Messages
63
Reaction score
0
Hey everyone, today in physics class, my teacher reduced a physics problem to solving a system of two equations in this form:

ax+by=c
ax2+by2=c

Where a, b, and c are constants. Then my teacher solved for x and y by solving for x in the first equation, plugging that into the second equation, resulting a very intimidating quadratic in y, and solving for y using the quadratic formula.

I was wondering if there was an easier way to solve for x and y in this situation. I have a feeling there would be some kind of a shortcut because of the similarities in the two equations.
 
Physics news on Phys.org
No, I think solving for either x or y in the first equation and then putting the result into the second is the simplest way to solve those equations.
 

Similar threads

Undergrad Canonical Form for quadratic equations *with* linear terms
  • · Replies 4 ·
Replies
4
Views
3K
High School Attempt to solve this system of three linear equations
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Solving a complex linear system with parameters
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Method to solve a coupled system of matrix equation
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Can this particular method solve these quadratic equations?
  • · Replies 11 ·
Replies
11
Views
2K
High School Need assistance with an unusual quadratic solution method
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Help solving a System of Linear Equations
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Solution?: Quintic Equation from Physical System
  • · Replies 4 ·
Replies
4
Views
2K
High School Understanding Invertible Matrices and Homogenous Systems
  • · Replies 15 ·
Replies
15
Views
2K
Graduate How to solve a very large overdetermined system numerically?
  • · Replies 1 ·
Replies
1
Views
3K