Section 3.1 Solving Systems of Linear Equations by the Graphing Method 239 Solving a System of Linear Functions by Graphing y 2x 1, f 1x2 3 g1x2 2x 1 5 4 y 1 21 1 Solving a System of Linear Equations by Graphing f 1x2 1 Solve the system by graphing. x 3y 6 Solution: To graph the lines, write each equation in slope-intercept form. x 3y 6 6y 2x 6 3y x 6 1 3 6y 6 3y 3 Because the lines have the same slope but different y-intercepts, they are parallel (Figure 3-4). Two parallel lines do not intersect, which implies that the system has no solution. The system is inconsistent. The solution set is the empty set,5 6. Skill Practice Solve the system by graphing. 5. 2y 2x x y 3 y 1 3 y x 2 x 1 2x 6 6 6 x 3 6 3 6y 2x 6 Example 4 Answers 4. {(1, 1)} 5. The solution set is { }. The system is inconsistent. 5 4 y 1 543 21 1 2 3 4 5 1 3 4 5 Figure 3-4 x 3 2 2 y x 1 13 y x 2 13 Figure 3-3 Solve the system. Solution: This first function can be written as .This is an equation of a horizontal line. Writing the second equation as we have a slope of 2 and a y-intercept of (0, 1). The graphs of the functions are shown in Figure 3-3. The point of intersection is (1, 3). Therefore, the solution set is 511, 326. Skill Practice Solve the system by graphing. 4. g 1x2 3x 4 y 3 Example 3 54 3 1 2 3 4 5 2 3 4 5 x 3 2 f(x) 3 g(x) 2x 1 (1, 3) TIP: The equations in Example 3 are independent because they represent different lines. The system is consistent because it has a solution.
miller_intermediate_algebra_4e_ch1_3
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