Answer 2. ea1, 1 2 bf Solving a System by the Addition Method Example 2 Solve the system by using the addition method. Solution: 4x 5y 2 3x 1 4y 4x 5y 2 4x 5y 2 3x 1 4y 3x 4y 1 Step 1: Write both equations in standard form. There are no fractions or decimals. We may choose to eliminate either variable. To eliminate x, change the coefficients Step 3: Multiply the first equation by 3. Multiply the second equation by 4. Step 4: Add the equations. Step 5: Solve for y. 4x 5y 2 12x 15y 6 3x 4y 1 12x 16y 4 12x 15y 6 12x 16y 4 y 2 Step 6: Substitute y 2 back into one of the original equations and solve for x. Step 7: Check the ordered pair (3, 2) in both original equations. Multiply by 3. Multiply by 4. 4x 5y 2 4x 5122 2 4x 10 2 4x 12 x 3 TIP: To eliminate the x variable in Example 2, both equations were multiplied by appropriate constants to create 12x and 12x. We chose 12 because it is the least common multiple of 4 and 3. We could have solved the system by eliminating the y variable. To eliminate y, we would multiply the top equation by 4 and the bottom equation by 5. This would make the coefficients of the y variable 20 and 20, respectively. 4 x 5y 2 16x 20y 8 3 x 4y 1 15x 20y 5 Skill Practice Solve by using the addition method. 2. 2y 5x 4 3x 4y 1 Section 3.3 Solving Systems of Linear Equations by the Addition Method 255 Multiply by 4. Multiply by 5. to 12 and 12. The solution set is 513, 226. y 2 TIP: The addition method works on the principle that adding the same quantity to both sides of an equation produces an equivalent equation. In step 4 of Example 2, the expressions 12x 15y and 6 are equal. These expressions are added vertically with the equation below to produce an equivalent equation.
miller_intermediate_algebra_4e_ch1_3
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