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quadratic formula: x = (-b +- √(b²-4ac)) / 2a
2 equations, for 2 unknowns (need n equations to solve for n unknowns)
Example: 5x + 2y = 7, 3x - y = 6 Solve by a) graphing both equations and see where they intersect (can graph multiple equations on desmos) b) substitution (using one equation set one variable in terms of the other, then substitute into the other equation): y = 3x-6 5x + 2(3x-6) = 7 11x - 12 = 7 c) addition - put all like terms in columns, multiply/divide as needed to get one set of terms to cancel add the terms, solve for the remaining term 5x + 2y = 7 6x - 2y = 12 -------------- 11x = 19, solve for x, then put in to find y
Define x and y in terms of t (time). Arrows on graph represent increasing values of t. Allows you to create functions, using two graphs, from things are not functions for both x and y together (circles, ellipses, x = y², etc)
Eliminating the parameter: substitute for t and define x in terms of y (or vice versa), aka rectangular equation.
https://courses.lumenlearning.com/suny-osalgebratrig/chapter/parametric-equations/