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Understanding Ordered Pairs and Solutions in Two-Variable Equations

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This lesson focuses on ordered pairs (x, y) and their role in locating points on a coordinate plane. Students will learn how to determine if a given ordered pair is a solution for a two-variable equation. The importance of the order of coordinates is emphasized, with examples of substituting x and y values into equations to verify solutions. Additionally, students will create tables of solutions to various equations such as y = x + 3 and y = 4x - 6. The activity aims to enhance students' understanding of coordinate systems and linear equations.

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Understanding Ordered Pairs and Solutions in Two-Variable Equations

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  1. Unit 4 Day 1 Notes

  2. An ordered pair (x, y) is a pair of numbers that can be used to locate a point on a coordinate plane. A solution of a two-variable equation can be written as an ordered pair.

  3. ? ? 11= 11 11 = 4(3) – 1 Helpful Hint The order in which a solution is written is important. Always write x first, then y. Determine whether each ordered pair is a solution of y = 4x – 1. (3, 11) y = 4x – 1 Substitute 3 for x and 11 for y. A solution since 11=11.  (3, 11) is a solution.

  4. ? 3 = 4(10) – 1 ? 3 = 39 Determine whether each ordered pair is a solution of y = 4x – 1. (10, 3) y = 4x – 1 Substitute 10 for x and 3 for y.  (10, 3) is not a solution.

  5. ? 38 = 5(7) + 3 ? 38 = 38 Determine whether each ordered pair is a solution of y = 5x + 3. (7, 38) y = 5x + 3 Substitute 7 for x and 38 for y.  (7, 38) is a solution.

  6. ? 17 = 5(9) + 3 ? 17 = 48 Determine whether each ordered pair is a solution of y = 5x + 3. (9, 17) y = 5x + 3 Substitute 9 for x and 17 for y.  (9, 17) is not a solution.

  7. Helpful Hint 1 A table of solutions can be set up vertically or horizontally. 2 3 4 Use the given values to make a table of solutions. y = x + 3for x = 1, 2, 3, 4 x x + 3 y (x, y) 1 + 3 4 (1, 4) 2 + 3 5 (2, 5) 3 + 3 6 (3, 6) 4 + 3 7 (4, 7)

  8. 1 2 3 4 Use the given values to make a table of solutions. y = x + 6for x = 1, 2, 3, 4 x x + 6 y (x, y) 1 + 6 7 (1, 7) 2 + 6 8 (2, 8) 3 + 6 9 (3, 9) 4 + 6 10 (4, 10)

  9. Determine whether each ordered pair is a solution of y = 4x  7. 1.(2, 15) 2. (4, 9) 3. Use the given values to make a table of solutions. y= 4x 6 for x = 2, 4, 6, 8, and 10 no yes

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