Solving a System of Equations by Elimination SYSTEMS1.2- I can solve a system of equation by elimination.

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Presentation transcript:

Solving a System of Equations by Elimination SYSTEMS1.2- I can solve a system of equation by elimination.

Vocabulary Elimination- to get rid of something. ( x or y ) Solving a system by elimination- Adding or subtracting equations together to get rid of x or y so that you can solve for the solution.

Ex 1: Elimination with Addition Solve the system of equations by elimination x + y = -2 x – y = 6 x + y = -2 + x – y = 6 2x + 0 = 4 2x = 4 Divide each side by 2 x = y = y = -4 y = -4 Final Answer: ( 2, -4)

When should I use addition? You should only add your system of equations together when there is the same variable with same coefficients with different signs… such as: y and –y 2x and – 2x 6y and -6y 4x and -4x

Ex. 2: Elimination with Subtraction Solve the system of equations by subtraction: x – 2y = -9 x + 3y = 16 x - 2 y = -9 - x + 3y = 16 -5y = -25 Divide each side by -5 y = 5 x – 2(5) = -9 x – 10 = x = 1 Final Answer: (1, 5)

When should I use subtraction? You should use subtraction when you have the same variable with the same coefficient and the same sign… such as.. 2x and 2x -y and –y -7x and -7x 3y and 3y

Ex. 3: Elimination when you have to multiply before you can add/subtract. Solve by Elimination: - x – 7y = x – 14y = 28 4(- x – 7y = 14) 1(- 4x – 14y = 28) - 4x + 28y = x – 14y = y = 48 Divide both sides by 14 y = 2 -x – 7(2) = 14 -x -14 = 14 -x = 0 x = 0 Final Answer (0, 2)

Think… Pair… Share… Explain to your neighbor how you know when you should add your system of equations to solve, when you should subtract your systems to solve, and when you slould use elimination.