Fri, 1/13 SWBAT… solve a system of equations using elimination by adding or subtracting Agenda 1. WU (10 min) 2. Three examples: elimination using addition.

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Presentation transcript:

Fri, 1/13 SWBAT… solve a system of equations using elimination by adding or subtracting Agenda 1. WU (10 min) 2. Three examples: elimination using addition or subtraction (20 min) 3. Practice – HW#4 Warm-Up: Negative three times one number plus five times another number is -11. Three times the first number plus 7 times the other number is -1. Find the numbers.

Ex.1: Elimination using Addition Negative three times one number plus five times another number is -11. Three times the first number plus 7 times the other number is -1. Find the numbers. -3x + 5y = -11 3x + 7y = -1 Q: What did you notice about the x coefficients? A: They were the opposite!

Ex. 2: Elimination using Subtraction 2t + 5r = 6 2t + 9r = 22 Q: What do you notice about the t coefficients? A: They are the same!

Ex. 2a: Elimination using Subtraction -2t + 5r = 6 -2t + 9r = 22 Q: What do you notice about the t coefficients? A: They are the same!

Addition or Subtraction? And Eliminate Which Variable 4x + 5y = 67 2x + 5y = 45 8x + 61y = 367 8x + 53y = 945 x + 7y = 72 -x - 8y = 34 5x - 9y = 67 2x + 9y = 45 45h + 73j = h + 73j = 42095

HW#3: Elimination Answers 1. (5, 2) 2. (1, 6) 3. (6, 1) 4. (-3, 5) 5. (4, -1) 6. (2, 3) 7. (6, 18)

Ex. 1a: Elimination using Multiplication (easiest to eliminate the y variables) 5x + 6y = -8 2x + 3y = -5

Ex. 1b: Elimination using Multiplication (eliminate the x variables) 5x + 6y = -8 2x + 3y = -5

Ex 2a: Elimination using Multiplication (Eliminate the x variables) 9x + 5y = 34 8x – 2y = -2

Ex 2b: Elimination using Multiplication (Eliminate the y variables) 9x + 5y = 34 8x – 2y = -2

Ex3a: Elimination using Multiplication (Eliminate the x variables) 3x + 3y = 9 4x + 2y = 8 Answer: (1, 2)

Ex3b: Elimination using Multiplication (Eliminate the y variables) 3x + 3y = 9 4x + 2y = 8 Answer: (1, 2)

-6x – 8y = x + 4y = 12 Multiply the second Equation by 2 Eliminate y

3x + 5y = 7 10x + 15y = 20 Multiply the first Equation by 3 Eliminate y

-9x – 8y = x - 7y = 19 Multiply the first Equation by 2 Eliminate x

-5x – 3y = 22 x - y = 10 Multiply the second equation by 5 Eliminate x Or Multiply the second equation by 3 Eliminate y

HW#4: Elimination Answers 1. (2, -3) 2. (1, 2) 3. c = 3.95, a = a.) (4, 1) d.) (0, 3) (2, 5)

HW#5: Any Method Answers 1. D 2. D 3. C

Ex. 1a: Elimination using Multiplication (eliminate the x variables) 5x + 6y = -8 2x + 3y = -5

Ex. 1b: Elimination using Multiplication (easiest to eliminate the y variables) 5x + 6y = -8 2x + 3y = -5

Ex 2a: Elimination using Multiplication (Eliminate the x variables) 9x + 5y = 34 8x – 2y = -2

Ex 2b: Elimination using Multiplication (Eliminate the y variables) 9x + 5y = 34 8x – 2y = -2

Ex 3a: Elimination using Multiplication (Eliminate the x variables) 3x + 3y = 9 4x + 2y = 8 Answer: (1, 2)

Ex 3b: Elimination using Multiplication (Eliminate the y variables) 3x + 3y = 9 4x + 2y = 8 Answer: (1, 2)