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Mastering Elimination Method for Solving Systems of Equations

Learn how to use elimination by multiplication to solve systems of equations efficiently. Understand the steps, examples, and solutions to tackle complex equations. Improve your mathematical skills today!

aimee-william
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Mastering Elimination Method for Solving Systems of Equations

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  1. Section 8.4 What we are Learning: Solving systems of equations using elimination by multiplication Determine the best method for solving systems of equations

  2. Which Method Should You Use to Solve a System of Equations?

  3. Elimination by Multiplication: • Make sure that equations are written in the same form. • Terms that have a variable in common need to be on the same side of the equation • Determine if the coefficients have a factor in common • Multiply each equation by the factor that will create a term with the same coefficient. • Be sure that one of the terms is positive and the other is negative • Solve the system of equations using elimination

  4. Examples: • 4x + 7y = 6 (-3) why? 6x + 5y = 20 (2) why? -12x – 21y = -18 12x + 10y = 40 -11y = 22 -11y/-11 = 22/-11 y = -2 4x + 7(-2) = 6 4x -14 = 6 4x -14 + 14 = 6 + 14 4x = 20 4x/4 = 20/4 x = 5 Solution: (5, -2) • 4x – 3y = 12 x + 2y = 14 (-4) why? 4x – 3y = 12 -4x – 8y = -56 -11y = -44 -11y/-11 = -44/-11 y = 4 4x – 3(4) = 12 4x – 12 = 12 4x – 12 + 12 = 12 + 12 4x = 24 4x/4 = 24/4 x = 6 Solution: (6, 4)

  5. Let’s Work These Together: • 9x = 5y – 2 3x = 2y – 2 2x + 3y = 20 4x + 7y =16

  6. Let’s Work This Together: 6x – 5y = 27 3x + 10y = -24 2x – 3y = 2 5x + 4y = 28

  7. Let’s Work This Together • The difference of four times a number and three times a second number is twelve. The first number added to two times the second number is 14. Find the two numbers.

  8. Homework: • Page 479 • 15 to 23 odd • 29, 31

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