CHAPTER 6 Summary 405 Section 6.7 Solving Systems of Equations by Graphing y x One solution Line 2 Consistent Line 1 y x Line 2 Inconsistent No solution Line 1 y x Line 2 Dependent Line 1 Infinite number of solutions Solving Systems of Equations by Algebraic Methods Substitution Addition (or elimination) method Discussion page 353 Example 2, page 354 Example 9, pages 359–360 Examples 3–5, pages 355–356 Examples 6–8, 10, pages 357–358, 360–361 Section 6.8 Linear Inequalities in Two Variables System of Linear Inequalities Graph both inequalities on the same axes. The solution is the set of points that satisfy both inequalities. Fundamental Principle of Linear Programming If the objective function K Ax By = + is evaluated at each point in a feasible region, the maximum and minimum values of the equation occur at vertices of the region. Examples 1–3, pages 367–368 Examples 4– 6, pages 368–370 Discussion pages 370–371 Examples 7– 8, pages 371–372 Section 6.9 Quadratic equation in one variable: ax bx c a 0, 0 2 + + = ≠ Quadratic formula: x b b ac a 4 2 2 = − ± − Zero-Factor Property If a b 0, ⋅ = then a 0 = or b 0. = Examples 8, 9, page 382 Examples 10, 11, pages 383–384 Example 7–8, pages 381–382 Section 6.10 Quadratic equation (or function) in two variables: y ax bx c a , 0 2 = + + ≠ Axis of symmetry of a parabola: x b a2 = − Exponential function: y a f x a a a or ( ) , 1, 0 x x = = ≠ > Exponential growth or decay formula: P t P a a a ( ) , 0, 1 kt 0 = > ≠ Natural exponential function: f x e e ( ) , 2.7183 x = ≈ Natural exponential growth or decay function: P t P e ( ) kt 0 = Examples 5–8, pages 390–393 Examples 5–8, pages 390–393 Examples 9–14, pages 396–399 Example 9, page 396 Examples 13, 14, page 399 Examples 13, 14, page 399
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