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256 Chapter 3 Systems of Linear Equations and Inequalities Solving a System by the Addition Method Solve the system by using the addition method. x 2y 6 y x 2y 6 y x 3y 6 0.05y 0.02x 0.10 0.02x 0.05y 0.10 0.02x 0.05y 0.10 2x5y10 x 3y 6 2x 6y 12 2x 5y 10 2x 5y 10 x 2y 6 y x 2122 6 122 x 4 4 x 0 0.2x 0.3y 1.5 y 2 2. Solving Inconsistent Systems and Systems of Dependent Equations Solving a System of Dependent Equations Solve the system by using the addition method. Solution: 1 5 x 1 2 y 1 4x 10y 20 1 5 1 2 x y 1 4x 10y 20 Example 4 Step 1: Equations are in standard form. Answer 3. {(0, 5)} Step 1: Write both equations in standard form. Step 2: Clear decimals. Step 3: Create opposite coefficients. Step 4: Add the equations. Step 5: Solve for y. Step 6: To solve for x, substitute into one of the original equations. y 2 Multiply by 100. Multiply by 2. Solution: Step 7: The ordered pair (0,2) checks in each original equation. The solution set is 510, 226. Skill Practice Solve by using the addition method. 3. 5x 3y 20 y y 2 x 3y 6 0.05y 0.02x 0.10 Example 3


miller_intermediate_algebra_4e_ch1_3
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