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CCGPS Coordinate Algebra (2-4-13)

CCGPS Coordinate Algebra (2-4-13). 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: When is it better to use substitution than elimination for solving systems?

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CCGPS Coordinate Algebra (2-4-13)

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  1. CCGPS Coordinate Algebra (2-4-13) 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: When is it better to use substitution than elimination for solving systems? Standard: MCC9-12.A.REI.6

  2. Solve Systems of Equations by Graphing

  3. Steps • Make sure each equation is in slope-intercept form: y = mx + b. • Graph each equation on the same graph paper. • The point where the lines intersect is the solution. If they don’t intersect then there’s no solution. • Check your solution algebraically.

  4. 1. Graph to find the solution. y = 3x – 12 y = -2x + 3 Solution: (3, -3)

  5. 2. Graph to find the solution. Solution: (-1, 3)

  6. 3. Graph to find the solution. No Solution

  7. 4. Graph to find the solution. Solution: (-3, 1)

  8. 5. Graph to find the solution. Solution: (-2, 5)

  9. Types of Systems • There are 3 different types of systems of linear equations 3 Different Systems: • Consistent-independent • Inconsistent • Consistent-dependent

  10. Type 1: Consistent-independent • A system of linear equations having exactly one solution is described as being consistent-independent. y  The system has exactly one solution at the point of intersection x

  11. Type 2: Inconsistent • A system of linear equations having no solutions is described as being inconsistent. y  The system has no solution, the lines are parallel x Remember, parallel lines have the same slope

  12. Type 3: Consistent-dependent • A system of linear equations having an infinite number of solutions is described as being consistent-dependent. y  The system has infinite solutions, the lines are identical x

  13. So basically…. • If the lines have the same y-intercept b, and the same slope m, then the system is consistent-dependent • If the lines have the same slope m, but different y-intercepts b, the system is inconsistent • If the lines have different slopes m, the system is consistent-independent

  14. Solve Systems of Equations by Substitution

  15. Steps • One equation will have either x or y by itself, or can be solved for x or y easily. • Substitute the expression from Step 1 into the other equation and solve for the other variable. • Substitute the value from Step 2 into the equation from Step 1 and solve. • Your solution is the ordered pair formed by x & y. • Check the solution in each of the original equations.

  16. Solve by Substitution 1. x = -4 3x + 2y = 20 1. (-4, 16)

  17. Solve by Substitution 2. y = x - 1 x + y = 3 2. (2, 1)

  18. Solve by Substitution 3. 3x + 2y = -12 y = x - 1 3. (-2, -3)

  19. Solve by Substitution 4. x = 1/2 y - 3 4x - y = 10 4. (8, 22)

  20. Solve by Substitution 5. x = -5y + 4 3x + 15y = -1 5. No solution

  21. Solve by Substitution 6. 2x - 5y = 29 x = -4y + 8 6. (12, -1)

  22. Solve by Substitution 7. x = 5y + 10 2x - 10y = 20 7. Many solutions

  23. Solve by Substitution 8. 2x - 3y = -24 x + 6y = 18 9. (-6, 4)

  24. CW/HW

  25. HW Graphing and Substitution WS

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