Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
1.5 Solving Linear Systems by Elimination The substitution method for solving a system of equations works well when at least one variable in one or both equations has a coefficient of 1 or -1. With other coefficients, substitution may lead to complicated equations with fractions. Is there another algebraic method that we can use? Yes! We can use the method of ELIMINATION. Example 1 Solve Solving by Addition 3x+2y = 19 (1) 5x-2y = 5 (2) 1 Step 1: Add equation (1) to equation (2). 3x+2y = 19 5x-2y =5 ______ 8x = 24 x=3 Adding the equations eliminates the y-terms and allows us to solve for x. Step 2: Substitute 3 for x in equation (1). 3(3)+2y = 19 9+2y = 19 2y = 10 y=5 2 Step 3: Check in equation (2). LS = 5x-2y = 5(3)-2(5) = 15 - 10 =5 RS = 5 ∴ the solution is (3,5) Example 2 Solve Solving by Subtraction 2x-3y = 12 (1) 5x-3y = 21 (2) 3 Example 3 Solve Using Multiplication and Subtraction Solve 3x+2y = 2 (1) 4x+5y = 12 (2) Example 4 Solve Using Multiplication and Subtraction Solve 0.3x-0.5y = 1.2 (1) 0.7x-0.2y = -0.1 (2) 4 Example 5 Solve Using Multiplication and Addition Solve 4a - _ b=9 (1) 3 4 _ _ 5a + b = 1 6 (2) 5