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Fun Practice with Simultaneous Equations for Edexcel A Level - Easy Steps and Answers!

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Safwan Master

05/04/2023

Maths

Simultaneous Equations Questions

Fun Practice with Simultaneous Equations for Edexcel A Level - Easy Steps and Answers!

A Level simultaneous equations practice guide covering various question types and solution methods.

  • Covers linear and non-linear simultaneous equations
  • Includes step-by-step solutions for complex problems
  • Demonstrates algebraic and graphical approaches
  • Incorporates real-world applications and exam-style questions
...

05/04/2023

692

SIMULTANEOUS EQUATIONS
1.
2.
3.
4.
Solve the simultaneous equations:
a)
b)
c)
y = 6-x
x² + y² = 20
y = x-5
y = x²5x12
2x + y = 11
xy = 15
a)

View

Page 2: Solving Linear and Quadratic Simultaneous Equations

This page demonstrates solutions for the first two problems, showcasing methods of solving simultaneous equations that combine linear and quadratic equations.

For the first problem y=6xandx2+y2=20y = 6 - x and x² + y² = 20, the solution process involves:

  1. Substituting the linear equation into the quadratic equation
  2. Simplifying and solving the resulting quadratic equation
  3. Finding the corresponding y-values

The second problem y=x5andy=x25x+12y = x - 5 and y = x² - 5x + 12 is solved by:

  1. Equating the two expressions for y
  2. Simplifying to form a quadratic equation
  3. Solving the quadratic and finding the corresponding y-values

Definition: A quadratic equation is a polynomial equation of the second degree, typically in the form ax² + bx + c = 0, where a ≠ 0.

Highlight: These solutions demonstrate the importance of algebraic manipulation and the application of quadratic solving techniques in A Level maths simultaneous equations.

SIMULTANEOUS EQUATIONS
1.
2.
3.
4.
Solve the simultaneous equations:
a)
b)
c)
y = 6-x
x² + y² = 20
y = x-5
y = x²5x12
2x + y = 11
xy = 15
a)

View

Page 3: Advanced Simultaneous Equations Techniques

This page continues with solutions to more complex simultaneous equations, including a system involving multiplication of variables xy=15xy = 15 and a problem requiring elimination of a variable.

The solution for 2x + y = 11 and xy = 15 involves:

  1. Expressing y in terms of x using the first equation
  2. Substituting this expression into the second equation
  3. Solving the resulting quadratic equation
  4. Finding the corresponding y-values

For the elimination problem, students are guided to:

  1. Substitute the expression for y into the second equation
  2. Simplify and rearrange to form a quadratic equation in x
  3. Solve the quadratic equation
  4. Express the solutions in the form a + b√3

Example: The solution x = 1 ± 2√3 demonstrates how A Level simultaneous equations questions and answers often involve surds and irrational numbers.

Highlight: These problems showcase the integration of various algebraic techniques, including substitution, elimination, and quadratic solving, essential for mastering Edexcel A Level simultaneous equations practice questions.

SIMULTANEOUS EQUATIONS
1.
2.
3.
4.
Solve the simultaneous equations:
a)
b)
c)
y = 6-x
x² + y² = 20
y = x-5
y = x²5x12
2x + y = 11
xy = 15
a)

View

Page 4: Graphical and Algebraic Approaches to Simultaneous Equations

This page introduces a combination of graphical and algebraic methods for solving simultaneous equations, particularly focusing on the intersection of linear and quadratic functions.

The problem involves solving:

  1. x + 2y = 3
  2. x² - 2y + 4y² = 18

The solution process demonstrates:

  1. Expressing y in terms of x using the linear equation
  2. Substituting this expression into the quadratic equation
  3. Solving the resulting fourth-degree equation

Additionally, the page introduces a problem involving the graphs of y = pxx and y = qxx, where:

  • pxx = 3 - ½x
  • qxx = x² - 10x - 20

Students are asked to:

  1. Solve qxx = 0, expressing the answer in surd form
  2. Sketch both graphs on the same axes
  3. Find the coordinates of intersection points algebraically

Vocabulary: The vertex of a parabola is the point where it turns, representing either a maximum or minimum point of the quadratic function.

Highlight: This page emphasizes the importance of combining graphical understanding with algebraic problem-solving in A Level maths simultaneous equations step by step solutions.

SIMULTANEOUS EQUATIONS
1.
2.
3.
4.
Solve the simultaneous equations:
a)
b)
c)
y = 6-x
x² + y² = 20
y = x-5
y = x²5x12
2x + y = 11
xy = 15
a)

View

Page 5: Graphical Interpretation and Complex Algebraic Solutions

This page continues the exploration of graphical and algebraic methods for solving simultaneous equations, focusing on the intersection of curves and lines.

The main problem involves finding the intersection points of:

  1. y = x² - 8x + 20 aparabolaa parabola
  2. y = x + 6 astraightlinea straight line

The solution process demonstrates:

  1. Equating the two equations
  2. Rearranging to form a quadratic equation
  3. Solving the quadratic to find x-coordinates
  4. Calculating corresponding y-coordinates

The page also introduces a more complex problem involving the intersection of:

  1. y = 3x - 2√x forx0for x ≥ 0
  2. y = 8x - 16

Example: The solution process for y = 3x - 2√x and y = 8x - 16 demonstrates how to handle equations involving square roots in simultaneous equations exam questions and solutions.

Highlight: These problems showcase the integration of algebraic and graphical techniques, essential for tackling complex Edexcel A Level simultaneous equations practice questions.

SIMULTANEOUS EQUATIONS
1.
2.
3.
4.
Solve the simultaneous equations:
a)
b)
c)
y = 6-x
x² + y² = 20
y = x-5
y = x²5x12
2x + y = 11
xy = 15
a)

View

Page 6: Advanced Techniques for Non-Linear Simultaneous Equations

This final page focuses on solving a challenging non-linear system of simultaneous equations, demonstrating advanced algebraic manipulation techniques.

The problem involves finding the intersection of:

  1. y = 3x - 2√x forx0for x ≥ 0
  2. y = 8x - 16

The solution process includes:

  1. Equating the two equations
  2. Rearranging to isolate the square root term
  3. Squaring both sides to eliminate the square root
  4. Solving the resulting quadratic equation in √x
  5. Verifying solutions and discarding invalid ones

Highlight: This problem exemplifies the level of complexity found in hard simultaneous equations questions and answers at the A Level, requiring a combination of algebraic skills and logical reasoning.

Vocabulary: Non-linear equations are those where the variables are not in a simple linear relationship, often involving powers, roots, or products of variables.

This page concludes the comprehensive guide on A Level simultaneous equations questions and answers, providing students with a robust set of techniques for tackling a wide range of problem types.

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Maths

692

5 Apr 2023

6 pages

Fun Practice with Simultaneous Equations for Edexcel A Level - Easy Steps and Answers!

S

Safwan Master

@safwanmaster

A Level simultaneous equations practice guide covering various question types and solution methods.

  • Covers linear and non-linear simultaneous equations
  • Includes step-by-step solutions for complex problems
  • Demonstrates algebraic and graphical approaches
  • Incorporates real-world applications and exam-style questions
SIMULTANEOUS EQUATIONS
1.
2.
3.
4.
Solve the simultaneous equations:
a)
b)
c)
y = 6-x
x² + y² = 20
y = x-5
y = x²5x12
2x + y = 11
xy = 15
a)

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Page 2: Solving Linear and Quadratic Simultaneous Equations

This page demonstrates solutions for the first two problems, showcasing methods of solving simultaneous equations that combine linear and quadratic equations.

For the first problem y=6xandx2+y2=20y = 6 - x and x² + y² = 20, the solution process involves:

  1. Substituting the linear equation into the quadratic equation
  2. Simplifying and solving the resulting quadratic equation
  3. Finding the corresponding y-values

The second problem y=x5andy=x25x+12y = x - 5 and y = x² - 5x + 12 is solved by:

  1. Equating the two expressions for y
  2. Simplifying to form a quadratic equation
  3. Solving the quadratic and finding the corresponding y-values

Definition: A quadratic equation is a polynomial equation of the second degree, typically in the form ax² + bx + c = 0, where a ≠ 0.

Highlight: These solutions demonstrate the importance of algebraic manipulation and the application of quadratic solving techniques in A Level maths simultaneous equations.

SIMULTANEOUS EQUATIONS
1.
2.
3.
4.
Solve the simultaneous equations:
a)
b)
c)
y = 6-x
x² + y² = 20
y = x-5
y = x²5x12
2x + y = 11
xy = 15
a)

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Improve your grades

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By signing up you accept Terms of Service and Privacy Policy

Page 3: Advanced Simultaneous Equations Techniques

This page continues with solutions to more complex simultaneous equations, including a system involving multiplication of variables xy=15xy = 15 and a problem requiring elimination of a variable.

The solution for 2x + y = 11 and xy = 15 involves:

  1. Expressing y in terms of x using the first equation
  2. Substituting this expression into the second equation
  3. Solving the resulting quadratic equation
  4. Finding the corresponding y-values

For the elimination problem, students are guided to:

  1. Substitute the expression for y into the second equation
  2. Simplify and rearrange to form a quadratic equation in x
  3. Solve the quadratic equation
  4. Express the solutions in the form a + b√3

Example: The solution x = 1 ± 2√3 demonstrates how A Level simultaneous equations questions and answers often involve surds and irrational numbers.

Highlight: These problems showcase the integration of various algebraic techniques, including substitution, elimination, and quadratic solving, essential for mastering Edexcel A Level simultaneous equations practice questions.

SIMULTANEOUS EQUATIONS
1.
2.
3.
4.
Solve the simultaneous equations:
a)
b)
c)
y = 6-x
x² + y² = 20
y = x-5
y = x²5x12
2x + y = 11
xy = 15
a)

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Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 4: Graphical and Algebraic Approaches to Simultaneous Equations

This page introduces a combination of graphical and algebraic methods for solving simultaneous equations, particularly focusing on the intersection of linear and quadratic functions.

The problem involves solving:

  1. x + 2y = 3
  2. x² - 2y + 4y² = 18

The solution process demonstrates:

  1. Expressing y in terms of x using the linear equation
  2. Substituting this expression into the quadratic equation
  3. Solving the resulting fourth-degree equation

Additionally, the page introduces a problem involving the graphs of y = pxx and y = qxx, where:

  • pxx = 3 - ½x
  • qxx = x² - 10x - 20

Students are asked to:

  1. Solve qxx = 0, expressing the answer in surd form
  2. Sketch both graphs on the same axes
  3. Find the coordinates of intersection points algebraically

Vocabulary: The vertex of a parabola is the point where it turns, representing either a maximum or minimum point of the quadratic function.

Highlight: This page emphasizes the importance of combining graphical understanding with algebraic problem-solving in A Level maths simultaneous equations step by step solutions.

SIMULTANEOUS EQUATIONS
1.
2.
3.
4.
Solve the simultaneous equations:
a)
b)
c)
y = 6-x
x² + y² = 20
y = x-5
y = x²5x12
2x + y = 11
xy = 15
a)

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Page 5: Graphical Interpretation and Complex Algebraic Solutions

This page continues the exploration of graphical and algebraic methods for solving simultaneous equations, focusing on the intersection of curves and lines.

The main problem involves finding the intersection points of:

  1. y = x² - 8x + 20 aparabolaa parabola
  2. y = x + 6 astraightlinea straight line

The solution process demonstrates:

  1. Equating the two equations
  2. Rearranging to form a quadratic equation
  3. Solving the quadratic to find x-coordinates
  4. Calculating corresponding y-coordinates

The page also introduces a more complex problem involving the intersection of:

  1. y = 3x - 2√x forx0for x ≥ 0
  2. y = 8x - 16

Example: The solution process for y = 3x - 2√x and y = 8x - 16 demonstrates how to handle equations involving square roots in simultaneous equations exam questions and solutions.

Highlight: These problems showcase the integration of algebraic and graphical techniques, essential for tackling complex Edexcel A Level simultaneous equations practice questions.

SIMULTANEOUS EQUATIONS
1.
2.
3.
4.
Solve the simultaneous equations:
a)
b)
c)
y = 6-x
x² + y² = 20
y = x-5
y = x²5x12
2x + y = 11
xy = 15
a)

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 6: Advanced Techniques for Non-Linear Simultaneous Equations

This final page focuses on solving a challenging non-linear system of simultaneous equations, demonstrating advanced algebraic manipulation techniques.

The problem involves finding the intersection of:

  1. y = 3x - 2√x forx0for x ≥ 0
  2. y = 8x - 16

The solution process includes:

  1. Equating the two equations
  2. Rearranging to isolate the square root term
  3. Squaring both sides to eliminate the square root
  4. Solving the resulting quadratic equation in √x
  5. Verifying solutions and discarding invalid ones

Highlight: This problem exemplifies the level of complexity found in hard simultaneous equations questions and answers at the A Level, requiring a combination of algebraic skills and logical reasoning.

Vocabulary: Non-linear equations are those where the variables are not in a simple linear relationship, often involving powers, roots, or products of variables.

This page concludes the comprehensive guide on A Level simultaneous equations questions and answers, providing students with a robust set of techniques for tackling a wide range of problem types.

SIMULTANEOUS EQUATIONS
1.
2.
3.
4.
Solve the simultaneous equations:
a)
b)
c)
y = 6-x
x² + y² = 20
y = x-5
y = x²5x12
2x + y = 11
xy = 15
a)

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Introduction to Simultaneous Equations

This page introduces a series of A Level simultaneous equations questions and answers, covering a range of difficulty levels and equation types. The problems presented include both linear and non-linear simultaneous equations, requiring students to apply various solving techniques.

Highlight: The questions progress from basic linear equations to more complex non-linear systems, providing a comprehensive practice set for A Level students.

Example: Question 1 asks students to solve y = 6 - x and x² + y² = 20, introducing the concept of combining linear and quadratic equations.

Vocabulary: Simultaneous equations refer to a set of equations that must be solved together to find values that satisfy all equations simultaneously.

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

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Stefan S

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This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

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Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

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Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

iOS user

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Sudenaz Ocak

Android user

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Greenlight Bonnie

Android user

very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

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