Solving Simultaneous Equations: x^2 + y^2 = 10 and y = 2x - 5

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Homework Help Overview

The discussion revolves around solving simultaneous equations, specifically the equations x^2 + y^2 = 10 and y = 2x - 5. Participants express a desire to understand the underlying concepts and methods for solving such equations independently.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster considers manipulating the equations, such as making a variable the subject or squaring an expression. Other participants inquire about the expression for y^2 and suggest substituting it into the first equation.

Discussion Status

The discussion is active, with participants exploring different approaches to substitute and manipulate the equations. There is a focus on understanding the process rather than reaching a definitive solution.

Contextual Notes

Participants emphasize the importance of understanding the methodology behind solving the equations, indicating a preference for learning over simply obtaining answers. There is a mention of the original poster's intent to grasp the concepts for future applications.

Haroldingo
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Homework Statement



Sure I could do this by looking at the mark scheme, but i need to know HOW and WHY, so that in the future i can do these equations by myself. Thanks :)

by elimenating y, solve the simeltaneous equation

Homework Equations



x^2 + y^2 = 10
y = 2x - 5

The Attempt at a Solution



I thought i might have to make 5 the subject for the equation for this to work?

Outside of this my solution was to square it but that didn't work either..
 
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If y = 2x - 5 , what is y2 ?
 
SammyS said:
If y = 2x - 5 , what is y2 ?
(2x - 5) 2 ?
 
Haroldingo said:
(2x - 5) 2 ?
Now replace y2 in the first equation with this expression, and solve the resulting quadratic.
 

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