By John L. Casti

Five Golden principles: nice Theories of 20th-Century arithmetic and Why They topic

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**Extra resources for 5 Golden Rules: Great Theories of 20th-Century Mathematics and Why They Matter**

**Example text**

B. y ϭ 2x ϩ 2 c. y ϭ 4x ϩ 2 The last two inequalities are included because x and y cannot be negative. 24. 24 In Example 3, the relationship between the year and the population was given by a table of values. In mathematics, the relationship between the variables x and y is often given by an equation, from which you can construct a table of values. Technology: Discovery Solution Begin by letting x and y represent the following. y Ordered Pairs as Solutions 2 Determine whether ordered pairs are solutions of equations.

254 square matrix, p. 254 augmented matrix, p. 255 coefficient matrix, p. 1 Systems of Equations row-equivalent matrices, p. 256 minor (of an entry), p. 268 Cramer’s Rule, p. 270 system of linear inequalities, p. 279 solution of a system of linear inequalities, p. 279 vertex, p. 280 218 1 Determine if ordered pairs are solutions of systems of equations. 2 Solve systems of equations graphically. 3 Solve systems of equations algebraically using the method of substitution. 4 Use systems of equations to model and solve real-life problems.

Determine whether ordered pairs are solutions of equations. Use the Distance Formula to find the distance between two points. Use the Midpoint Formula to find the midpoints of line segments. 2 Graphs of Equations 140 1 Sketch graphs of equations using the point-plotting method. 2 Find and use x- and y-intercepts as aids to sketching graphs. 3 Use a pattern to write an equation for an application problem, and sketch its graph. Assignment Completed S24 * Available for purchase. com/pic/larsonIASSE4e.