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messersmith_power_introductory_algebra_1e_ch4_7_10

YOU TRY 1 Solve the system by the substitution method. 3x 4y 2 6x y 3 If no variable in the system has a coeffi cient of 1 or 1, solve for any variable. 2 Solve a System Containing Fractions or Decimals If a system contains an equation with fractions, fi rst multiply the equation by the least common denominator to eliminate the fractions. Likewise, if an equation in the system contains decimals, begin by multiplying the equation by the lowest power of 10 that will eliminate the decimals. Solve the system by the substitution method. 3 10 x 1 5 y 1 (1) 1 12 x 1 3 y 5 6 (2) Solution Before applying the steps for solving the system, eliminate the fractions in each equation. 3 10 x 1 5 y 1 1 12 x 1 3 y 5 6 10 x 1 5 yb 10 1 Multiply by the LCD: 10. 12 a 1 12 x 1 3 yb 12 5 6 Multiply by 3x 2y 10 (3) Distribute. x 4y 10 (4) Distribute. From the original equations, we obtain an equivalent system of equations. 3x 2y 10 (3) x 4y 10 (4) the LCD: 12. Now, we will work with equations (3) and (4). Apply the steps for solving the system: Step 1: The x in equation (4) has a coeffi cient of 1. Solve this equation for x. x 4y 10 Equation (4) x 10 4y Subtract 4y. x 10 4y Divide by 1. Step 2: Substitute 10 4y for x in equation (3). 3x 2y 10 (3) 3(10 4y) 2y 10 Substitute. Step 3: Solve the equation above for y. 3(10 4y) 2y 10 30 12y 2y 10 Distribute. 30 10y 10 Combine like terms. 10y 40 Add 30 to each side. y 4 Divide by 10. EXAMPLE 3 In-Class Example 3 Solve the system by the substitution method. 1 12 x 1 4 y 3 2 2 5 x 1 2 y 3 Answer: (0, 6) 10 a 3 Review the eliminating fractions from an equation procedure that you learned in Section 2.3. www.mhhe.com/messersmith SECTION 4.2 Solving Systems by the Substitution Method 257


messersmith_power_introductory_algebra_1e_ch4_7_10
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