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Ch 2 – Systems of Linear Equations & Inequalities

Ch 2 – Systems of Linear Equations & Inequalities. 2.1 – Solving Systems of Equations in Two Variables. Consistent: Independent: Dependent: Inconsistent:. A system of equations with at least one solution. A system of equations with exactly one solution.

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Ch 2 – Systems of Linear Equations & Inequalities

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  1. Ch 2 – Systems of Linear Equations & Inequalities 2.1 – Solving Systems of Equations in Two Variables

  2. Consistent: • Independent: • Dependent: • Inconsistent: A system of equations with at least one solution. A system of equations with exactly one solution. A system of equations with infinitely many solutions. aka coincide A system of equations with no solutions. Vocabulary

  3. Draw a graphical picture of the four vocabulary words.

  4. There are 3 ways to solve linear systems: 1. Graphically 2. Substitution 3. Elimination

  5. When solving graphically, you look for the intersection of the two lines (if there is any) Graphically

  6. The goal of substitution is to put one equation into the other so there is only one variable to solve for. Substitution

  7. The goal with elimination is to get one variable to cancel by adding the two equations together or a multiple of the two equations. • Then you will only have 1 equation with 1 unknown and you can solve for it. Elimination

  8. x = 5 4x + 5y = 20 Solve the system graphically

  9. Solve the linear system by substitution. x + 3y = 0 2x + 6y = 5

  10. Solve by elimination. 3x – 5y = -8 x + 2y = 1

  11. 1. x = 2y – 8 2x – y = 7 Solve the following linear systems.

  12. 2. 3x + 2y = 10 5x - 7y = -4

  13. 3. 6x – 4y = 14 -3x + 2y = 7

  14. 4. 9x – 3y = 15 -3x + y = -5

  15. Madison is thinking about leasing a car for two years. The dealership says that they will lease her the car she has chosen for $326 per month with only $200 down. However, if she pays $1600 down, the lease payment drops to $226 per month. • What is the break-even point in the two lease plans that Madison is considering? • If Madison keeps the lease for 24 months, which lease should she choose?

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