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miller_intermediate_algebra_4e_ch1_3

250 Chapter 3 Systems of Linear Equations and Inequalities Solve by using the substitution method. 4x 2y 6 Solving a System of Dependent Equations 4x 2y 6 4x 212x 32 2x 3 6 Step 3: Solve for x. Apply the distributive property to clear the parentheses. 4x 4x 6 6 The system reduces to the identity Therefore, the two equations are equivalent. The solution set consists of all points on the common line, giving us an infinite number of solutions. The equations are dependent and because the equations 4x 2y 6 and y 3 2x represent the same line, the solution set can be written as 51x, y2 51x, y2 0 y 3 2x6 0 4x 2y 66 or Skill Practice Solve the system by using substitution. 4. 3x 6y 12 2y x 4 6 6. 6 6 TIP: We can confirm the results of Example 4 by writing each equation in slopeintercept form. The slope-intercept forms are identical, indicating that the lines are the same. slope-intercept form 4x 2y 6 2y 4x 6 y 2x 3 y 3 2x y 2x 3 Solution: Step 1: Solve for one of the variables. Step 2: Substitute the quantity for y in the other equation. y 3 2x y 2x 3 v y 3 2x Example 4 Answer 4. Infinitely many solutions; ; 51x, y2 0 3x 6y 126 dependent equations


miller_intermediate_algebra_4e_ch1_3
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