Linear and Quadratic Simultaneous Equations Flashcards

A set of two or more equations with two or more variables that are solved together to find a common solution.

An equation where the highest power of the variable is 1, e.g., y = 2x + 3.

An equation where the highest power of the variable is 2, e.g., y = x² + 3x + 2.

A method to solve simultaneous equations by substituting one equation into the other to eliminate a variable.

A method to solve simultaneous equations by adding or subtracting equations to eliminate one variable (used for linear equations only).

1. Rearrange the linear equation to make one variable the subject. 2. Substitute into the quadratic equation. 3. Solve the resulting quadratic equation. 4. Substitute back to find the other variable.

There can be 0, 1, or 2 solutions depending on whether the line intersects the parabola.

The discriminant (b² - 4ac) determines the number of solutions: > 0 means 2 solutions, = 0 means 1 solution, < 0 means no solutions.

The solutions are the points where the straight line intersects the parabola on a graph.

Linear: y = 2x + 1, Quadratic: y = x² + 3x + 2. Solve by substitution: 2x + 1 = x² + 3x + 2.