Algebra 1 Notes Lesson 7-3 Elimination Using Addition and Subtraction

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Mathematics Standards Patterns, Functions and Algebra: Add, subtract, multiply and divide monomials and polynomials. Patterns, Functions and Algebra: Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions. Patterns, Functions and Algebra: Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology. Patterns, Functions and Algebra: Solve real world problems that can be modeled using systems of linear equations and inequalities.

Vocabulary Elimination – Third method to solve system of equations. Add or subtract equations. First was Graphing. Second was Substitution.

Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 3x – 6y = 18

Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 3x – 6y = 18

Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 (+) 3x – 6y = 18 -2y =

Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 (+) 3x – 6y = 18 -2y = 30 -2 -2 y = -15

Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 (+) 3x – 6y = 18 -2y = 30 -2 -2 y = -15

Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 -3x + 4(-15) = 12 (+) 3x – 6y = 18 -2y = 30 -2 -2 y = -15

Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 -3x + 4(-15) = 12 (+) 3x – 6y = 18 -3x – 60 = 12 -2y = 30 -2 -2 y = -15

Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 -3x + 4(-15) = 12 (+) 3x – 6y = 18 -3x – 60 = 12 -2y = 30 +60 +60 -2 -2 y = -15

Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 -3x + 4(-15) = 12 (+) 3x – 6y = 18 -3x – 60 = 12 -2y = 30 +60 +60 -2 -2 -3x = 72 y = -15

Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 -3x + 4(-15) = 12 (+) 3x – 6y = 18 -3x – 60 = 12 -2y = 30 +60 +60 -2 -2 -3x = 72 y = -15 -3 -3

Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 -3x + 4(-15) = 12 (+) 3x – 6y = 18 -3x – 60 = 12 -2y = 30 +60 +60 -2 -2 -3x = 72 y = -15 x = -24 -3 -3

Example 1 Use elimination to solve the system of equations. -3x + 4y = 12 -3x + 4(-15) = 12 (+) 3x – 6y = 18 -3x – 60 = 12 -2y = 30 +60 +60 -2 -2 (-24, -15) -3x = 72 y = -15 x = -24 -3 -3

Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x – 3y = 18

Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x – 3y = 18

Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 (–) 4x – 3y = 18 5y =

Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 (–) 4x – 3y = 18 5y = 10

Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 (–) 4x – 3y = 18 5y = 10 5 5 y = 2

Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 (–) 4x – 3y = 18 5y = 10 5 5 y = 2

Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x + 2(2) = 28 (–) 4x – 3y = 18 5y = 10 5 5 y = 2

Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x + 2(2) = 28 (–) 4x – 3y = 18 4x + 4 = 28 5y = 10 5 5 y = 2

Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x + 2(2) = 28 (–) 4x – 3y = 18 4x + 4 = 28 5y = 10 – 4 – 4 5 5 y = 2

Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x + 2(2) = 28 (–) 4x – 3y = 18 4x + 4 = 28 5y = 10 – 4 – 4 5 5 4x = 24 y = 2

Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x + 2(2) = 28 (–) 4x – 3y = 18 4x + 4 = 28 5y = 10 – 4 – 4 5 5 4x = 24 y = 2 4 4 x = 6

Example 2 Use elimination to solve the system of equations. 4x + 2y = 28 4x + 2(2) = 28 (–) 4x – 3y = 18 4x + 4 = 28 5y = 10 – 4 – 4 5 5 4x = 24 y = 2 4 4 (6, 2) x = 6

Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n

Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m

Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 2n

Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 2n + 3m

Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 2n + 3m = 6

Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 2n + 3m = 6

Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 (+) 2n + 3m = 6 6n = 18 6 6 n = 3

Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 (+) 2n + 3m = 6 6n = 18 6 6 n = 3

Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 4(3) – 3m = 12 (+) 2n + 3m = 6 6n = 18 6 6 n = 3

Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 4(3) – 3m = 12 (+) 2n + 3m = 6 12 – 3m = 12 6n = 18 6 6 n = 3

Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 4(3) – 3m = 12 (+) 2n + 3m = 6 12 – 3m = 12 6n = 18 – 12 – 12 6 6 n = 3

Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 4(3) – 3m = 12 (+) 2n + 3m = 6 12 – 3m = 12 6n = 18 – 12 – 12 6 6 -3m = 0 n = 3

Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 4(3) – 3m = 12 (+) 2n + 3m = 6 12 – 3m = 12 6n = 18 – 12 – 12 6 6 -3m = 0 n = 3 m = 0

Example 3 Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers. 4n – 3m = 12 4(3) – 3m = 12 (+) 2n + 3m = 6 12 – 3m = 12 6n = 18 – 12 – 12 6 6 -3m = 0 n = 3 3 and 0 m = 0

Example 4 2x + 3y = 7 7x + 2y = 32

Example 4 2x + 3y = 7 7x + 2y = 32 Uh Oh……

Example 4 2x + 3y = 7 7x + 2y = 32 Uh Oh…… We will learn how to solve these in the next section.

Homework Pg. 385 12-32 (evens) 34,35, and 40