5.3 Elimination Using Addition and Subtraction Objective: Each student will understand when to solve a system by elimination using addition and subtraction. Academic Standard:2.4d Solve systems of equations. Algebra 1

Notes: Another algebraic method used to solve systems of equations. - two equations are combined by either addition or subtraction to eliminate one of the variable - then substitute that value back into either of the original equations. - the solution is written as an ordered pair If the coefficients of one of the variables are additive inverses , or opposites. variables are the same. What is the Elimination Method? When should you use addition? When should you use subtraction?

Example 1 : Use elimination to solve the system 5x + 3y = 6 -5x + y = 2 + -5x + y = 2 4y = 8 y = 2 5x + 3(2) = 6 5x + 6 = 6 5x = 0 x = 0 Since 5x and -5x are additive inverses we will add the two equations together. Add equations Divide both sides by 4 y = 2 Substitute 2 in for y in one of the original equations Subtract 6 from both sides Divide by 5 on both sides Solution (0 , 2)

Practice 1: Use elimination to solve the system of equations. 3x – 5y = -16 2x + 5y = 31 -4x – 3y = -3 4x – 5y = 5

Example 2: Twice a number added to another number is 18 Example 2: Twice a number added to another number is 18. Four times the first number minus the other number is 12. Find the numbers? Define variables: x = first number y = second number Write a verbal expression for each equation Twice a number added to another number is 18. Four times the first number minus the other number is 12. Write an algebraic expression for each equation 2x + y = 18 4x + y = 12 Solve using elimination

Assignment Pg 268 (1-4, 8-16 even, 37-42)