Simultaneous Equations - One Linear, One Non-linear Simplified Revision Notes for Leaving Cert Mathematics

Revision notes with simplified explanations to understand Simultaneous Equations - One Linear, One Non-linear quickly and effectively.

Learn about Simultaneous Equations for your Leaving Cert Mathematics Exam. This Revision Note includes a summary of Simultaneous Equations for easy recall in your Mathematics exam

450+ students studying

Simultaneous Equations - One Linear, One Non-linear

In this case of simultaneous equations, we will be faced with solving a pair of equations in which one equation is linear and one is non-linear.

Consider these cases :

We notice two points of intersection for each of the diagrams.

Example

infoNote

Solve the pair of simultaneous equations :

x + 2y = 8 \quad \text{(Equation A)} \\ x^2 + y^2 = 52 \quad \text{(Equation B)}

Solve for one variable :

x + 2y = 8

x = 8 - 2y

Substitute into the other equation :

x^2 + y^2 = 52

(8 - 2y)^2 + y^2 = 52

Expand and simplify :

64 - 32y + 4y^2 + y^2 = 52

64 - 32y + 5y^2 = 52

5y^2 - 32y + 12 = 0

Solve :

y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

y = \frac{-(-32) \pm \sqrt{(-32)^2 - 4(5)(12)}}{2(5)}

y = \frac{32 + 28}{10} = \frac{60}{10} = :success[6]

y = \frac{32 - 28}{10} = \frac{4}{10} = :success[0.4]

Solve for $x$ :

x = 8 - 2y

x = 8 - 2(6) = 8 - 12 = :success[-4]

x = 8 - 2(0.4) = 8 - 0.8 = :success[7.2]

Solutions :

(x, y) = :success[(-4, 6)] \quad \text{and} \quad :success[(7.2, 0.4)].

500K+ Students Use These Powerful Tools to Master Simultaneous Equations - One Linear, One Non-linear For their Leaving Cert Exams.

Enhance your understanding with flashcards, quizzes, and exams—designed to help you grasp key concepts, reinforce learning, and master any topic with confidence!

127 flashcards

Flashcards on Simultaneous Equations - One Linear, One Non-linear

Revise key concepts with interactive flashcards.

Try Mathematics Flashcards

10 quizzes

Quizzes on Simultaneous Equations - One Linear, One Non-linear

Test your knowledge with fun and engaging quizzes.

Try Mathematics Quizzes

29 questions

Exam questions on Simultaneous Equations - One Linear, One Non-linear

Boost your confidence with real exam questions.

Try Mathematics Questions