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miller_intermediate_algebra_4e_ch1_3

Section 3.3 Solving Systems of Linear Equations by the Addition Method 257 10 a 2x 5y 10 1 4x 10y 20 Multiply by 10. Multiply by 2. 2x 5y 10 4 x 10y 20 4x 10y 20 4x 10y 20 0 0 Step 2: Clear fractions. Step 3: Multiply the first equation by 2. Step 4: Add the equations. Notice that both variables were eliminated. The system of equations is reduced to the identity Therefore, the two original equations are dependent. The solution set consists of an infinite number of ordered pairs (x, y) that fall on the common line of intersection or equivalently The solution set is 4x 10y 20, y 1. 0 0. Skill Practice Solve by the addition method. 4. 3x y 4 x 1 3 y 4 3 or e 1x, y2 ` 1 5 x 1 2 15 x 12 51x, y2 0 4x 10y 206 y 1 f 5 x 1 2 yb 10 1 2y 3x 4 2016x 5y2 40 20y Example 5 3x 2y 4 3x 2y 4 Step 3: Divide the 120x 80y 40 3x 2y 1 Divide by 40. 0 3 second equation by 40. Step 4: Add the equations. 5 4 y 1 120x 80y 40 21 Answers 4. Infinitely many solutions; 0 {(x, y) 3x y 4}; dependent equations 5. No solution; { }; inconsistent system With both equations now in standard form,we can proceed with the addition method. Step 2: The goal is to create opposite coefficients on either the x or y terms.The second equation can be divided by 40. The equations reduce to a contradiction, indicating that the system has no solution.The system is inconsistent.The two equations represent parallel lines, as shown in Figure 3-8. There is no solution,5 6. Skill Practice Solve by using the addition method. 5. 18 10x 6y 5x 3y 9 543 1 2 3 4 5 1 3 4 5 x 3 2 2 3x 2y 4 Figure 3-8 Solving an Inconsistent System Solve the system by using the addition method. Solution: Step 1: Write the equations in standard form. 2y3x4 3x 2y4 2016x5y2 4020y 120x100y 40 20y 120x80y 40


miller_intermediate_algebra_4e_ch1_3
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