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Solving Systems of Equations: Methods, Examples, and Practice Problems

This lesson provides a comprehensive overview of solving systems of equations using various methods such as substitution and elimination. Through several examples, students will learn how to set up equations based on word problems involving two numbers, their sums, and differences. Practice problems are included to reinforce learning. Key objectives are to identify variables, formulate equations, and solve for unknowns. Homework assignments will focus on applying these methods, ensuring a solid understanding before the upcoming quiz.

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Solving Systems of Equations: Methods, Examples, and Practice Problems

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  1. Warmups – Solve using any method. • y = x – 6 2) x – y = 5 3) 4x + 5y = 12 3x – 2y = 7 2x – 3y = 7 4x + 3y = 4

  2. Homework Questions?

  3. Word Problems Objective: To solve word problems involving systems of equations.

  4. WORDS THAT MEAN . . .

  5. EXAMPLE 1 Solve using . . . substitution Don’t forget, you get 2 answers: y = 10, x = 15 You do not have to write these as an ordered pair. 1) Two numbers have a sum of 25. One number is 5 more than the other number. Find the numbers. Pick 2 variables x and y Write 2 equations x + y = 25 x = 5 + y

  6. EXAMPLE 2 Solve using . . . elimination Don’t forget, you get 2 answers: x = 18, y = 12 2) The difference of two numbers is 6. Their sum is 30. Find the two numbers. Pick 2 variables x and y Write 2 equations x – y = 6 x + y = 30

  7. EXAMPLE 3 Solve using . . . substitution Don’t forget, you get 2 answers: y = 3, x = 12 3) The sum of two numbers is 15. One number is 4 times the other. Find the numbers. Pick 2 variables x and y Write 2 equations x + y = 15 x = 4y

  8. TOO: The sum of two numbers is 32. The difference between the two numbers is 8. Find the numbers. 20, 12 Three times the first number plus the second number equals 20. Five times the first number minus the second number equals 12. Find the numbers. 4, 8

  9. HOMEWORK • Solving Problems with System of Equations • Do both sides • Tell me if you used substitution (S) or elimination (E) QUIZ next week  Yippee!

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