Pre-Algebra 1-7 Ordered Pairs Learn to write solutions of equations in two variables as ordered pairs.

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Presentation transcript:

Pre-Algebra 1-7 Ordered Pairs Learn to write solutions of equations in two variables as ordered pairs.

Pre-Algebra 1-7 Ordered Pairs An ordered pair is the pair of plugged in numbers that makes and equation true. Our goal is to find x and y numbers that plug into the equation and work. If they do, the ordered pair is a solution to the equation. Is (7, 15) a solution?  15 = = 15 Yes! Is (6, 13) a solution?  13 = = 14 No! y = x + 8 (x, y)  Ordered pair y = x + 8(x, y)

Pre-Algebra 1-7 Ordered Pairs Determine whether the ordered pair (3, 11) is a solution of y = 4x – 1. Additional Example 1A: Determining If an Ordered Pair Is a Solution of an Equation A. (3, 11) y = 4x – 1 11 = 4(3) – 1Substitute 3 for x and 11 for y. 11= 11  (3, 11) is a solution to y = 4x – 1. A solution since 11=11. x y

Pre-Algebra 1-7 Ordered Pairs Determine whether the ordered pair (11, 3) is a solution of y = 4x – 1. Additional Example 1B: Determining If an Ordered Pair Is a Solution of an Equation B. (11, 3) y = 4x – 1 3 = 4(11) – 1Substitute 11 for x and 3 for y. 3 = 43  (11, 3) is not a solution to y = 4x – 1. x y

Pre-Algebra 1-7 Ordered Pairs Determine whether the ordered pair (7, 38) is a solution of y = 5x + 3. Try This: Example 1A A. (7, 38) y = 5x = 5(7) + 3Substitute 7 for x and 38 for y. 38 = 38  (7, 38) is a solution to y = 5x + 3. x y

Pre-Algebra 1-7 Ordered Pairs Determine whether the ordered pair (30, 9) is a solution of y = 3x + 3. Try This: Example 1B B. (30, 9) y = 3x = 3(30) + 3Substitute 30 for x and 9 for y. 9 = 93  (30, 9) is not a solution to y = 3x + 3. x y

Pre-Algebra 1-7 Ordered Pairs Use the given values to make a table of ordered pair solutions. Additional Example 2A: Creating a Table of Ordered Pair Solutions A. y = 7x for x = 1, 2, 3, 4 x7x7xy(x, y) (1)7(1, 7) 7(2)14(2, 14) 7(3)21(3, 21) 7(4)28(4, 28) These four ordered pairs are all solutions that make y = 7x work.

Pre-Algebra 1-7 Ordered Pairs Use the given values to make a table of ordered pair solutions. A. y = 6x – 3 for x = 1, 2, 3, 4 x6x - 3y(x, y) (1) – 3 = 6 – 3 =3(1, 3) 6(2) – 3 = 12 – 3 = 9 (2, 9) 6(3) – 3 = 18 – 3 =15(3, 15) 6(4) – 3 = 24 – 3 =21(4, 21) Try This: Example 2A These 4 ordered pairs are solutions that make y=6x-3 work.

Pre-Algebra 1-7 Ordered Pairs Use the given values to make a table of ordered pair solutions. B. y = 8x + 2 for x = 1, 2, 3, (1) + 28(2) + 28(3) (1, 10) (2, 18) (3, 26) (4, 34) 8(4) + 2 x123 8x + 2 y (x, y) 4 Try This: Example 2B

Pre-Algebra 1-7 Ordered Pairs Partner Questions Determine whether each ordered pair is a solution for y = 4x  (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, 10 yesno x4x – 6y(x, y) 2 4(2)  6 2(2, 2) 4 4(4)  6 10(4, 10) 6 4(6)  6 18(6, 18) 8 4(8)  6 26(8, 26) 10 4(10)  6 34(10, 34)