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Transcript

Solving Sytems by Using Elimination ***Sometimes you get an equation with fractions when you solve for one of the variables in a linear system. These systems may be easier to solve using the linear combination method. Steps to Solving a Linear System by Linear Combinations Arrange the equations in standard form with like terms in columns. Step 1 Step 2 If necessary, make like terms “cancel out” by multiplying one or both equations by a number. Step 3 Add the two equations together. Solve for the remaining variable. Step 4 Step 5 Substitute the value obtained in step four into one of the original equations. Solve for the variable. Step 6 Step 7 Check. Example 1: Elimination Using Addition –x + 2y = -8 4x + 3y = 16 x + 6y = -16 Try These 1. 3x – 5y = -16 2x – 3y = 8 2x + 5y = 8 2. 2x + y = 18 4x – y = 12 Example 2: Elimination Using Subtraction 1. 3x + y = 5 2x + y = 10 2. 2x – 5y = -6 2x – 7y = -14 Try These 1. 2x – 6y = 6 2x + 3y = 24 2. 5x + 3y = 22 5x – 2y = 2 Example 3: Put in Standard Form First 1. y = –x – 4 x–y=2 Try These 1. 2x = 3y – 11 x + 3y = 8 2. 3x = 4 – y –y = –2x + 6 2. y = –9 – 4x –10 – 2y = 4x Example 4: Use a Linear System as a Real-World Model 1. The sum of two numbers is 48, and their difference is 24. the numbers? What are 3. Find two numbers whose sum is 51 and whose difference is 13. Example 1: Multiply One Equation to Eliminate 1. 3x + 4y = 6 5x + 2y = -4 2. 2y + y = 23 3x + 2y = 37 Try These 3. -5x + 3y = 6 Example 2: x–y=4 4. 2x + y = 5 3x – 2y = 4 Multiply Both Equations to Eliminate 3. 3x + 4y = -25 2x – 3y = 6 Try These 3. 2x – 3y = 2 5x + 4y = 28 4. 4x + 3y = 8 3x – 5y = -23 4. 4x – 7y = 10 3x + 2y = 14 Example 3: Use a Linear System as a Real-World Model 1. Eight times a number plus five times another number is -13. The sum of the two numbers is 1. What are the numbers? 2. Two times a number plus three times another number equals 4. Three times the first number plus four times the other number is 7. Find the numbers.