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

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SUMMARY

The discussion focuses on solving the simultaneous equations x² + y² = 10 and y = 2x - 5. The user seeks a comprehensive understanding of the solution process rather than just the answer. The recommended approach involves substituting y from the second equation into the first, resulting in the equation x² + (2x - 5)² = 10. This leads to a quadratic equation that can be solved for x, ultimately allowing for the determination of y.

PREREQUISITES
  • Understanding of quadratic equations
  • Familiarity with substitution methods in algebra
  • Knowledge of expanding binomials
  • Basic skills in solving simultaneous equations
NEXT STEPS
  • Practice solving quadratic equations using the quadratic formula
  • Learn about the method of substitution in greater detail
  • Explore the concept of graphing simultaneous equations
  • Study the properties of conic sections related to circles
USEFUL FOR

Students studying algebra, educators teaching simultaneous equations, and anyone looking to strengthen their problem-solving skills in mathematics.

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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