YOU TRY 1 Determine whether (4, 3) is a solution of each system of equations. a) 3x 5y 3 b) y 1 2 x 5 2 x y 5 x 3y 13 Let’s begin solving systems of equations by graphing. 2 Solve a Linear System by Graphing To solve a system of equations in two variables means to fi nd the ordered pair (or pairs) that satisfi es each equation in the system. Recall from Chapter 3 that the graph of a linear equation is a line. This line represents all solutions of the equation. x y 5 (2, 3) x 2y 8 5 5 y x 1 5 If two lines intersect at one point, that point of intersection is a solution of each equation. For example, the graph shows the lines representing the two equations in Example 1a). The solution to that system is their point of intersection, (2, 3). Notice that when you are solving a system of two linear equations, you are trying to find the intersection of the two lines. Definition When solving a system of equations by graphing, the point of intersection is the solution of the system. If a system has at least one solution, we say that the system is consistent. The equations are independent if the system has one solution. EXAMPLE 2 In-Class Example 2 Solve the system by graphing. y x 4 2x y 1 Solve the system by graphing. y 1 3 x 2 2 x 3y 3 Solution Graph each line on the same axes. The fi rst equation is in slope-intercept form, and we see that m 1 3 and b 2. Its graph is in blue. 246 CHAPTER 4 Linear Equations and Inequalities in Two Variables www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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