“ ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������ ����������������������������������������������������������������������������������������������������������������������������” �������������������������������������������������������������������������������� �� ���������������� �������� Equations and the Rectangular Coordinate System ����������������������������we studied linear equations in one variable. In this chapter, we will focus on linear equations in two variables. We will also study real-life applications of these equations and introduce the concept of a function. The following line graph shows the average cost of a 30-sec Super Bowl advertisement for 2002 to 2010. This is an example of a graph that we will learn how to read to obtain specific information. Average Cost of a 30-sec Super Bowl Ad, in Millions (2002–2010) 3.1 3 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2 2002 2003 2004 2005 2006 2007 2008 2009 2010 Verifying Solutions of Equations Algebraically In Chapter 2, we studied linear equations with one variable and learned how to find solutions of these equations. We found that a linear equation in one variable has one solution with the exception of identities and contradictions. Identities are satisfied by all real numbers and contradictions do not have a solution. In this chapter, our attention turns to equations with two variables. Some examples of equations in two variables are x + y = 3 y = 4x - 1 2x - 3y = 6 y = x2 + 2x - 3 Equations containing two variables have pairs of numbers that satisfy the equation. This pair of numbers is called an ordered pair and is denoted by (x, y), where x and y are the variables in the equation. A solution of an equation containing two variables is an ordered pair (x, y) that satisfies the equation. Consider the equation x + y = 3. Solutions of this equation must satisfy the fact that the sum of the x and y values is 3. Some solutions are (1, 2), (3, 0), (-1, 4), and (5, -2). We know these ordered pairs are solutions because they make the equation true when we replace the variables with their given values as shown in the following table. (x, y) x + y = 3 Solution? (1, 2) 1 + 2 = 3 3 = 3 Yes (3, 0) 3 + 0 = 3 3 = 3 Yes (-1, 4) -1 + 4 = 3 3 = 3 Yes (5, - 2) 5 + (-2) = 3 3 = 3 Yes ▶ OBJECTIVES As a result of completing this section, you will be able to 1. Determine algebraically if an ordered pair is a solution of an equation. 2. Plot ordered pairs and identify quadrants. 3. Graph the solutions of an equation. 4. Determine graphically if an ordered pair is a solution of an equation. 5. Solve application problems. 6. Troubleshoot common errors. Objective 1 ▶ Determine algebraically if an ordered pair is a solution of an equation. 194
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