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Solving simultaneous equations

Solving Quadratic Simultaneous Equations Step by Step for Kids

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Solving Quadratic Simultaneous Equations Step by Step for Kids
user profile picture

Shaz

@shaz2007

·

26 Followers

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A comprehensive guide to solving quadratic simultaneous equations step by step, focusing on various methods and worked examples.

  • Learn essential techniques for factorising and solving quadratic equations examples through detailed explanations
  • Understand the process of rearranging equations to solve simultaneous equations with both linear and quadratic components
  • Master the substitution method for solving systems of equations where one equation is quadratic and the other is linear
  • Explore different approaches to solving equations involving x² and y² terms
  • Practice with multiple worked examples demonstrating various solution methods and equation types

03/03/2023

564

Quadratic Simultaneous Equations (e.g. Solve the simultaneous equations: As both of these equations are equal to y. put them equal to each o

View

Page 2: Advanced Techniques for Quadratic Simultaneous Equations

This page covers more complex scenarios in solving quadratic simultaneous equations, particularly focusing on equations involving x² and y² terms.

Example: Solving x² + y² = 13 and x = y - 5

  1. Substitute x = y - 5 into x² + y² = 13
  2. Expand (y - 5)² + y² = 13
  3. Solve 2y² - 10y + 12 = 0
  4. Factorise and find y values
  5. Substitute back to find x values

Highlight: When dealing with equations containing both x² and y² terms, try to express one variable in terms of the other before substituting.

Definition: The substitution method involves replacing one variable with an equivalent expression to reduce the system to a single equation.

Vocabulary: Standard form - the arrangement of a quadratic equation in the form ax² + bx + c = 0.

Quadratic Simultaneous Equations (e.g. Solve the simultaneous equations: As both of these equations are equal to y. put them equal to each o

View

Page 1: Solving Basic Quadratic Simultaneous Equations

This page introduces fundamental methods for solving quadratic simultaneous equations through detailed worked examples. The content demonstrates how to solve equations where one equation is quadratic and the other is linear.

Definition: Quadratic simultaneous equations are systems of equations where at least one equation contains terms with variables squared.

Example: Solving y = x² - 8 and y = 3x + 10

  1. Equate the equations: x² - 8 = 3x + 10
  2. Rearrange to standard form: x² - 3x - 18 = 0
  3. Factorise: (x - 6)(x + 3) = 0
  4. Solve for x: x = 6 or x = -3
  5. Substitute back to find y values

Highlight: When solving quadratic simultaneous equations, always start by making the equations equal to each other if they both contain y terms.

Vocabulary: Factorisation - breaking down an algebraic expression into a product of simpler expressions.

Similar content

Know Simultaneous Equations Examples - National 5 Maths thumbnail

6

177

S4

Simultaneous Equations Examples - National 5 Maths

jotter scan from the topic simultaneous equations from the national 5 maths course. Includes worked examples :)

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Subjects

/

Maths

/

Algebra

/

Solving simultaneous equations

Solving Quadratic Simultaneous Equations Step by Step for Kids

user profile picture

Shaz

@shaz2007

·

26 Followers

Follow

A comprehensive guide to solving quadratic simultaneous equations step by step, focusing on various methods and worked examples.

  • Learn essential techniques for factorising and solving quadratic equations examples through detailed explanations
  • Understand the process of rearranging equations to solve simultaneous equations with both linear and quadratic components
  • Master the substitution method for solving systems of equations where one equation is quadratic and the other is linear
  • Explore different approaches to solving equations involving x² and y² terms
  • Practice with multiple worked examples demonstrating various solution methods and equation types

03/03/2023

564

 

11/12

 

Maths

9

Quadratic Simultaneous Equations (e.g. Solve the simultaneous equations: As both of these equations are equal to y. put them equal to each o

Page 2: Advanced Techniques for Quadratic Simultaneous Equations

This page covers more complex scenarios in solving quadratic simultaneous equations, particularly focusing on equations involving x² and y² terms.

Example: Solving x² + y² = 13 and x = y - 5

  1. Substitute x = y - 5 into x² + y² = 13
  2. Expand (y - 5)² + y² = 13
  3. Solve 2y² - 10y + 12 = 0
  4. Factorise and find y values
  5. Substitute back to find x values

Highlight: When dealing with equations containing both x² and y² terms, try to express one variable in terms of the other before substituting.

Definition: The substitution method involves replacing one variable with an equivalent expression to reduce the system to a single equation.

Vocabulary: Standard form - the arrangement of a quadratic equation in the form ax² + bx + c = 0.

Quadratic Simultaneous Equations (e.g. Solve the simultaneous equations: As both of these equations are equal to y. put them equal to each o

Page 1: Solving Basic Quadratic Simultaneous Equations

This page introduces fundamental methods for solving quadratic simultaneous equations through detailed worked examples. The content demonstrates how to solve equations where one equation is quadratic and the other is linear.

Definition: Quadratic simultaneous equations are systems of equations where at least one equation contains terms with variables squared.

Example: Solving y = x² - 8 and y = 3x + 10

  1. Equate the equations: x² - 8 = 3x + 10
  2. Rearrange to standard form: x² - 3x - 18 = 0
  3. Factorise: (x - 6)(x + 3) = 0
  4. Solve for x: x = 6 or x = -3
  5. Substitute back to find y values

Highlight: When solving quadratic simultaneous equations, always start by making the equations equal to each other if they both contain y terms.

Vocabulary: Factorisation - breaking down an algebraic expression into a product of simpler expressions.

Similar content

Maths - Simultaneous Equations Examples - National 5 Maths

jotter scan from the topic simultaneous equations from the national 5 maths course. Includes worked examples :)

6

177

0

Know Simultaneous Equations Examples - National 5 Maths thumbnail

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

15 M

Pupils love Knowunity

#1

In education app charts in 12 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.