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1.9 Solving Linear Systems by Elimination

1.9 Solving Linear Systems by Elimination. Example: Solve the following system of equations:. x + y = 5 (1). x – y = 1 (2). 2 x = 6. Add equations (1) and (2). x = 3. 3 + y = 5 (1). Sub x = 3 in (1). y = 5 – 3. y = 2. Solution: (3, 2).

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1.9 Solving Linear Systems by Elimination

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  1. 1.9 Solving Linear Systems by Elimination Example: Solve the following system of equations: x + y = 5 (1) x – y = 1 (2) 2x = 6 Add equations (1) and (2) x = 3 3 + y = 5 (1) Sub x = 3 in (1) y = 5 – 3 y = 2 Solution: (3, 2)

  2. Example 2: Solve for x and y. 2x + 3y = 2 (1) 5x – y = 22 (2) 15x – 3y = 66 (2) Multiply (2) by 3 2x + 3y = 2 (1) 17x = 68 Add x = 4 2(4) + 3y = 2 Sub x = 4 in (1) 8 + 3y = 2 3y = 2 – 8 3y = – 6 Solution: (4, – 2) y = – 2

  3. Example 3: Solve for x and y. 3x + 4y = 11 (1) 5x + 7y = 20 (2) – 15x – 20y = – 55 (1) (1) by – 5 15x + 21y = 60 (2) (2) by 3 y = 5 Add Sub in (1) 3x + 4(5) = 11 3x + 20 = 11 3x = 11 – 20 3x = – 9 Sol: (– 3, 5) x = – 3

  4. 4x + 3y = 18 (2) y = 2 Example 4: Solve for x and y. 4(x + 1) + 3(y – 2) = 16 (2) 4x + 4 + 3y – 6 = 16 (2) 4x + 3y = 16 + 2 (2) 4x + 3y = 18 (2) 3×(1) 18x – 15y = 24 5×(2) 20x + 15y = 90 38x = 114 Solution (3, 2) x = 3

  5. The cost of admission to an NAC concert was $15 for students and $60 for adults. If there were 724 people at the concert and there was $33 945 in ticket sales, how many students attended the concert. Let x = number of students Let y = number of adults x + y = 724 (1) 15x + 60y = 33 945 (2) –60(1) – 60x – 60y = – 43440 (1) 15x + 60y = 33 945 (2) – 45x = – 9 495 x = 211 211 students

  6. 2x + 3y = 5 (1) 3x + 5y = 9 (2) Solve by Elimination 2x = 5 – 3y (1) 3x + 5y = 9 (2)

  7. 2x + 3y = 5 (1) 3x + 5y = 9 (2) Quiz 1) Solve by Elimination 2x = 5 – 3y (1) 3x + 5y = 9 (2) 2) If 6 pens and 4 pencils cost $13.26, and 4 pens and 6 pencils cost $9.40, find the cost of each.

  8. Solve by Elimination 2x + 3y = 5 (1) 3x + 5y = 9 (2) 6x + 9y = 15 (2) Multiply (1) by 3 – 6x – 10y = – 18 (1) Multiply (2) by – 2 – y = – 3 Add y = 3 2x + 3(3) = 5 Sub y = 3 in (1) 2x + 9 = 5 2x = 5 – 9 2x = – 4 Solution: (– 2, 3) x = – 2

  9. If 6 pens and 4 pencils cost $12.10, and 4 pens and 6 pencils cost $9.40, find the cost of each. Let x = number of pens Let y = number of pencils 6x + 4y = 12.10 (1) 4x + 6y = 9.40 (2) –2(1) – 12x – 8y = – 24.20 (1) 3(2) 12x + 18y = 28.20 (2) 10y = 4 y = 0.40 6x + 4(.4) = 12.10 (1) x = 1.75 $1.75, $0.40

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