CCGPS Coordinate Algebra

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Presentation transcript:

CCGPS Coordinate Algebra UNIT QUESTION: How do I justify and solve the solution to a system of equations or inequalities? Standard: MCC9-12.A.REI.1, 3, 5, 6, and 12 Today’s Question: Does multiplying an equation by a constant change the solution to a system of equations? Standard: MCC9-12.A.REI.5

Solve Systems of Equations by Elimination

Steps for Elimination: Arrange the equations with like terms in columns Multiply, if necessary, to create opposite coefficients for one variable. Add the equations. Substitute the value to solve for the other variable. Check

EXAMPLE 1 (continued) (-1, 3)

EXAMPLE 2 4x + 3y = 16 2x – 3y = 8 (4, 0)

EXAMPLE 3 3x + 2y = 7 -3x + 4y = 5 (1, 2)

EXAMPLE 4 2x – 3y = 4 -4x + 5y = -8 (2, 0)

EXAMPLE 5 5x + 2y = 7 -4x + y = –16 (3, -4)

EXAMPLE 5 2x + 3y = 1 4x – 2y = 10 (2, -1)

Classwork (-1, 4) (-1, 2) (-2, 2) (1, 5) (5, -2) (4, -1) (-1/2, 4) Add/Subtract Use elimination to solve each system of equations. 6x + 5y = 4 2. 3m – 4n = -14 3. 3a + b = 1 6x – 7y = -20 3m + 2n = -2 a + b = 3 -3x – 4y = -23 5. x – 3y = 11 6. x – 2y = 6 -3x + y = 2 2x – 3y = 16 x + y = 3 2a – 3b = -13 8. 4x + 2y = 6 9. 5x – y = 6 2a + 2b = 7 4x + 4y = 10 5x + 2y = 3 (-1, 4) (-1, 2) (-2, 2) (1, 5) (5, -2) (4, -1) (-1/2, 4) (1/2, 2) (1, -1)

Classwork (1, 1) (-3, 4) (-1, 2) (-1, 2) (4, -2) (-4, -2) (2, -1) Multiply Use elimination to solve each system of equations. 2x + 3y = 6 2. 2m + 3n = 4 3. 3a - b = 2 x + 2y = 5 -m + 2n = 5 a + 2b = 3 4x + 5y = 6 5. 4x – 3y = 22 6. 3x – 4y = -4 6x - 7y = -20 2x – y = 10 x + 3y = -10 4x – y = 9 8. 4a – 3b = -8 9. 2x + 2y = 5 5x + 2y = 8 2a + 2b = 3 4x - 4y = 10 (1, 1) (-3, 4) (-1, 2) (-1, 2) (4, -2) (-4, -2) (2, -1) (-1/2, 2) (2.5, 0)

Homework Practice Worksheet