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6.3 Solving Systems Using Elimination

6.3 Solving Systems Using Elimination. Standard: SWBAT solve a system of two linear equations in two variables algebraically. Mini Quiz 52. Is (-3, 1) a solution to the System of Equations:. 2. Quick Review. 1 . How do you solve by Substitution?

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6.3 Solving Systems Using Elimination

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  1. 6.3 Solving Systems Using Elimination Standard: SWBAT solve a system of two linear equations in two variables algebraically.

  2. Mini Quiz 52 • Is (-3, 1) a solution to the System of Equations: 2.

  3. Quick Review • 1. How do you solve by Substitution? • Pick an equation, substitute, solve, substitute and solve, check • 2. When is the answer “no solution”? • When the graph doesn’t touch or when the equation does not equal. • When is the answer “infinitely many solutions”? • When there is only one graph or when the equation equals on both sides.

  4. Linear Combination…Addition Method…Elimination… • Line up the terms (i.e. Ax + By = C) • Make one of the terms opposite (either the x’s or y’s) • Add the equations (to eliminate one of the variables) • Substitute answer (to find the other variable) • Check!

  5. Opposites! Quick Review: Tell me the opposite of each 1. 9 • -30 • 2x • -28y -9 30 -2x 28y

  6. Line Up • Make Opposite • 3. Add Equations • 4. Substitute • 5. Check Solve UsingLinear Combination -x + 2y = -8 x + 6y = -16 5. x – 2y = 8 6y + x = -16 x – 2y = 8 x + 6y = -16 -1 8y = -24 y = -3 x – 2y = 8 x – 2(-3) = 8 x + 6 = 8 x = 2 (2, -3) Check (2,-3) x – 2y = 8 2 – 2(-3) = 8 2 + 6 = 8 8 = 8  6y + x = -16 6(-3) + (2) = -16 -18 + 2 = -16 -16 = -16 

  7. Line Up • Make Opposite • 3. Add Equations • 4. Substitute • 5. Check Solve UsingLinear Combination 6. 4x + 3y = 16 2x – 3y = 8 7. r + t = 1 r – 2t = -2 8. 2m + 5n = -22 10m + 3n = 22 (4, 0) (0,1) (4, -6)

  8. Line Up • Make Opposite • 3. Add Equations • 4. Substitute • 5. Check Solve UsingLinear Combination 9. -2g + 15h = -32 7g – 5h = 17 10. 4a + 2b = 14 7a – 3b = -8 (1, -2) (1, 5)

  9. Line Up • Make Opposite • 3. Add Equations • 4. Substitute • 5. Check Solve UsingLinear Combination 11. -x + y = 1 x = y + 1 12. 2x – 4 = -y -2x – y = -4 13. x = -y + 8 y + x + 1= 0 No Solution Infinite Solutions No Solution

  10. Application 14. Suppose your community center sells a total of 292 tickets for a basketball game. An adult ticket costs $3. A student ticket costs $1. The sponsors collect $470 in ticket sales. Write and solve a system to find the number of each type of ticket sold. a = number of adult tickets s = number of student tickets a + s = 292 3a + 1s = 470 (89, 203)

  11. Wrap Up Elimination (Linear Combination/Addition Method) • Line up (i.e. Ax + By = C) • Make opposite • Add the equations • Substitute answer • Check! No Solution – x and y cancels and both sides are not equal Infinitely Many Solution – x and y cancels and both sides are equal HW: P. 290 #1-6 all, 48, 49, 51-61 odd. DLUQ: What do we need to find in order to eliminate one of the variables?

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