Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication

Mathematics Standards -Number, Number Sense and Operations: Explain the effects of operations such as multiplication or division, and of computing the powers and roots on the magnitude of quantities. -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.

Mathematics Standards -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.

Elimination with Multiplication One more step than before

Example 1 Use elimination to solve the system of equations. 2x +y = 23 3x + 2y = 37 multiply by 2

Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 2y = 46 3x + 2y = 37

Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 2y = 46 3x + 2y = 37 keep the same

Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 2y = 46 3x + 2y = 37 3x + 2y = 37

Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 2y = 46 3x + 2y = 37 (–)3x + 2y = 37 x = 9

Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 2y = 46 3x + 2y = 37 (–)3x + 2y = 37 x = 9

Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 2y = 46 3x + 2y = 37 (–)3x + 2y = 37 3(9) + 2y = 37 x = 9.

Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 2y = 46 3x + 2y = 37 (–)3x + 2y = 37 3(9) + 2y = 37 x = y = 37

Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 2y = 46 3x + 2y = 37 (–)3x + 2y = 37 3(9) + 2y = 37 x = y = 37 – 27 – 27

Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 2y = 46 3x + 2y = 37 (–)3x + 2y = 37 3(9) + 2y = 37 x = y = 37 – 27 – 27 2y = 10

Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 2y = 46 3x + 2y = 37 (–)3x + 2y = 37 3(9) + 2y = 37 x = y = 37 – 27 – 27 2y =

Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 2y = 46 3x + 2y = 37 (–)3x + 2y = 37 3(9) + 2y = 37 x = y = 37 – 27 – 27 2y = y = 5

Example 1 Use elimination to solve the system of equations. 2x +y = 23 multiply by 24x + 2y = 46 3x + 2y = 37 (–)3x + 2y = 37 3(9) + 2y = 37 x = y = 37 – 27 – 27 (9, 5) 2y = y = 5

Example 2 Use elimination to solve the system of equations. 4x + 3y = 8 3x – 5y = -23

Example 2 Use elimination to solve the system of equations. 4x + 3y = 8multiply by 3 3x – 5y = -23

Example 2 Use elimination to solve the system of equations. 4x + 3y = 8multiply by 3 12x + 9y = 24 3x – 5y = -23

Example 2 Use elimination to solve the system of equations. 4x + 3y = 8multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4

Example 2 Use elimination to solve the system of equations. 4x + 3y = 8multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 412x – 20y = -92

Example 2 Use elimination to solve the system of equations. 4x + 3y = 8multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4 (-)12x – 20y = y = y = 4

Example 2 Use elimination to solve the system of equations. 4x + 3y = 8multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4 (-)12x – 20y = y = y = 4

Example 2 Use elimination to solve the system of equations. 4x + 3y = 8multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4 (-)12x – 20y = -92 3x – 5(4) = y = y = 4

Example 2 Use elimination to solve the system of equations. 4x + 3y = 8multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4 (-)12x – 20y = -92 3x – 5(4) = y = 116 3x – 20 = y = 4

Example 2 Use elimination to solve the system of equations. 4x + 3y = 8multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4 (-)12x – 20y = -92 3x – 5(4) = y = 116 3x – 20 = y = 4 3x =

Example 2 Use elimination to solve the system of equations. 4x + 3y = 8multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4 (-)12x – 20y = -92 3x – 5(4) = y = 116 3x – 20 = y = 4 3x = x = -1

Example 2 Use elimination to solve the system of equations. 4x + 3y = 8multiply by 3 12x + 9y = 24 3x – 5y = -23 multiply by 4 (-)12x – 20y = -92 3x – 5(4) = y = 116 3x – 20 = y = 4 3x = x = -1(-1, 4)

Example 3 Determine the best method to solve the system of equations. Then solve the system. x + 5y = 4 3x – 7y = -10

Example 3 Three Options: Graphing – Rarely best Substitution – If variable is solved for or easily solved for Elimination – If variable has same coefficient or solving for a variable gives a fraction

Example 3 Determine the best method to solve the system of equations. Then solve the system. x + 5y = 4 3x – 7y = -10 The best method to use is substitution because the coefficient of x in the first equation is 1, which makes it easy to solve for.

Example 3 x + 5y = 43x – 7y = -10 – 5y – 5y x = 4 – 5y

Example 3 x + 5y = 43x – 7y = -10 – 5y – 5y x = 4 – 5y

Example 3 x + 5y = 43x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y

Example 3 x + 5y = 43x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y

Example 3 x + 5y = 43x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y12 – 15y – 7y = – 22y = -10 – 12 – y = y = 1

Example 3 x + 5y = 43x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y12 – 15y – 7y = – 22y = -10 – 12 – y = y = 1

Example 3 x + 5y = 43x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y12 – 15y – 7y = -10 x = 4 – 5(1) 12 – 22y = -10 – 12 – y = y = 1

Example 3 x + 5y = 43x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y12 – 15y – 7y = -10 x = 4 – 5(1) 12 – 22y = -10 x = 4 – 5 – 12 – y = y = 1

Example 3 x + 5y = 43x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y12 – 15y – 7y = -10 x = 4 – 5(1) 12 – 22y = -10 x = 4 – 5 – 12 – 12 x = y = y = 1

Example 3 x + 5y = 43x – 7y = -10 – 5y – 5y 3(4 – 5y) – 7y = -10 x = 4 – 5y12 – 15y – 7y = -10 x = 4 – 5(1) 12 – 22y = -10 x = 4 – 5 – 12 – 12 x = y = -22 (-1, 1) y = 1

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