Section 3.2 Solving Systems of Linear Equations by the Substitution Method 249 2. Solving Inconsistent Systems and Systems of Dependent Equations Solving an Inconsistent System Example 3 Solve the system by using the substitution method. Solution: x 2y 4 2x 4y 6 Step 1: The x variable is already isolated. x 2y 4 2x 4y 6 212y 42 x 2y 4 4y 6 Step 2: Substitute the quantity into the other equation. Step 3: Solve for y. The equation reduces to a contradiction, indicating that the system has no solution. 4y 8 4y 6 8 6 There is no solution. The lines never intersect and must be The system is inconsistent. parallel.The system is inconsistent. The solution set is 5 6. TIP: The answer to Example 3 can be verified by writing each equation in slope-intercept form and graphing the equations. Equation 1 Equation 2 x 2y 4 2x 4y 6 2y x 4 4y 2x 6 4y 4 y 2x 4 1 2 x 6 4 3 2 y 1 2 x 2 5 4 3 2 1 1 1 Notice that the equations have the same slope, but different y-intercepts; therefore, the lines must be parallel. There is no solution to this system of equations. 2y 2 x 2 4 2 Answer 3. No solution; { }; inconsistent system y x 4 3 1 2 3 4 5 2 3 4 2 x 2y 4 2x 4y 6 5 Skill Practice Solve by using the substitution method. 3. 8x 16y 3 y 1 2 x 1
miller_intermediate_algebra_4e_ch1_3
To see the actual publication please follow the link above