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Solving Systems of Equations: The Substitution Method

Solving Systems of Equations: The Substitution Method. Example 1. Solve using substitution. y = 3x. 2x + 4y = 28. y = 3x. 2x + 4(3x) = 28. y = 3(2). 2x + 12x = 28. y = 6. 14x = 28. x = 2. (2,6). REMEMBER To Check: Always plug solution into original equations . Example 2.

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Solving Systems of Equations: The Substitution Method

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  1. Solving Systems of Equations:The Substitution Method

  2. Example 1 Solve using substitution. y = 3x 2x + 4y = 28 y = 3x 2x + 4(3x) = 28 y = 3(2) 2x + 12x = 28 y = 6 14x = 28 x = 2 (2,6) REMEMBER To Check: Always plug solution into original equations

  3. Example 2 Solve using substitution. 2x + y = 13 4x – 3y = 11 y = -2x + 13 4x – 3(-2x + 13) = 11 4x + 6x – 39 = 11 10x – 39 = 11 10x = 50 x = 5 2x + y = 13 2(5) + y = 13 (5,3) 10 + y = 13 y = 3

  4. Example 3 Solve using substitution. The sum of a number and twice another number is 13. The first number is 4 larger than the second number. What are the numbers? Let x = the first number Let y = the second number x + 2y = 13 y + 4 + 2y = 13 x = y + 4 3y + 4 = 13 3y = 9 y = 3 x = y + 4 x = 3 + 4 x = 7

  5. Practice Solve using substitution. 2) a – b = 4 3x + 4y = 2 • x + y = 5 x – 2y = 8 b = 2 – 5a 2x – y = 5 x = y + 1 2x + y = 8 3) 4) Translate to a system of equations and solve. • The sum of two numbers is 84. One number is three times the other. • Find the numbers.

  6. Practice Solve using substitution. 6) x= ½y + 3 7) 8x + 2y = 13 2x – y = 6 4x + y = 11

  7. Practice Translate to a system of equations and solve. 5) The sum of two numbers is 84. One number is three times the other. Find the numbers.

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