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.

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.