240 Chapter 3 Systems of Linear Equations and Inequalities Solving a System of Linear Equations by Graphing Example 5 Solve the system by graphing. x 4y 8 y 1 4 x 2 Solution: Write the first equation in slope-intercept form.The second equation is already in slope-intercept form. First equation Second equation 4y x 8 4y 4 Notice that the slope-intercept forms of the two lines are identical. Therefore, the equations represent the same line (Figure 3-5). The equations are dependent, and the solution to the system of equations is the set of all points on the line. 5 4 y 1 21 Because the ordered pairs in the solution set cannot all be listed, we can write the solution in set-builder notation. Furthermore, the equations and represent the same line.Therefore, the solution set may be written 14 x 2 x 26 y 51x, y2 51x, y2 0 x 4y 86. 0 y 14 as or Skill Practice Solve the system by graphing. 6. y 1 2 x 1 x 2y 2 x 4y 8 y 1 4 x 2 x 4 8 4 y 1 4 x 4y 8 x 2 Figure 3-5 Answer 6. Infinitely many solutions; 0 y 1 2 {(x, y) x 1 }; dependent equations 5 43 1 2 3 4 5 1 3 4 5 x 3 2 2 y x 2 14 Topic: Using the Intersect Feature The solution to a system of equations can be found by using either a Trace feature or an Intersect feature on a graphing calculator to find the point of intersection between two curves. For example, consider the system 2x y 6 5x y 1 Calculator Connections
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