Simultaneous Equations – One Linear, One Quadratic (Leaving Cert Mathematics): Flashcards

Straight line

Curves (circles, parabolas, hyperbolas)

Intersection points where line meets curve

Substitution method

Express one variable in terms of other (from linear eq)

Substitute into quadratic eq and solve

Find corresponding values for other variable

$x^2 + y^2 = r^2$ (r is radius)

$y = ax^2 + bx + c$ or $y = x^2$

Two solutions (most common case)

One solution (touches at exactly one point)

Linear equation (easier to rearrange)

Factorising quadratic expressions

$a^2 - 2ab + b^2$