5.4 Elimination Using Multiplication Algebra 1 Objective: Each student will understand if addition and subtraction does not eliminate a variable – how.

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Presentation transcript:

5.4 Elimination Using Multiplication Algebra 1 Objective: Each student will understand if addition and subtraction does not eliminate a variable – how they can use multiplication to solve real world problems. Academic Standard:2.4d Solve systems of equations.

Notes: When should I use the method of elimination using multiplication? How do I use the method of elimination using multiplication? What do I do next? If the coefficients of one of the variables are not additive inverses or not the same. Multiply each term of one equation by the same number, or, multiply both equations by different numbers in order to have one of the variables have coefficients that are additive inverses of each other or the same number. Use the elimination method using addition and subtraction to find the solution.

Example 1: Use elimination to solve the system 3x + 4y = 6 5x + 2y = -4 3x + 4y = 6 -2(5x + 2y = -4) 3x + 4y = 6 -10x - 4y = 8 -7x = 14 x = -2 No coefficients are additive inverses or the same Multiply the second equation by -2 Add the two equations Divide both sides by -7 3x + 4y = 6 3(-2) + 4y = y = 6 4y = 12 y = 3 Substitute x = -2 in to one of the original equations Add 6 to both sides Divide both sides by 4 Solution: (-2, 3)

Practice 1: Use elimination to solve the system a) 5x + 3y = 8 x + y = 2 b) 3x + 4y = -25 2x – 3y = 6

Practice 2: Use elimination to solve the system a)2x – 5y = 11 3x + 2y = 26 b) 4x + 6y = 26 2x + 3y = 13

Example 2: The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended? Define variables: a = adult tickets c = children’s tickets Write a verbal expression for each equation children tickets plus adult tickets is 2200 tickets 1.50 times children tickets plus 4.00 times adult tickets is $5050 Write an algebraic expression for each equation c + a = c + 4a = 5050 Solve using elimination

Assignment Pg , 8-16 even, 37-42