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Substitution: 4x+ 2y = 40 x+y = 13 -x -x y=-x+13 4x + 2(-x+13)=40 4x-2x+26 = 40 2x+26= 40

Once upon a time Old MacDonald had a farm. On his farm he had ducks that went a quack, quack here and cows that went a moo, moo there. He loved each one of his animals very much, so much he had a name for each of them. (13 names in all.)

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Substitution: 4x+ 2y = 40 x+y = 13 -x -x y=-x+13 4x + 2(-x+13)=40 4x-2x+26 = 40 2x+26= 40

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  1. Once upon a time Old MacDonald had a farm. On his farm he had ducks that went a quack, quack here and cows that went a moo, moo there. He loved each one of his animals very much, so much he had a name for each of them. (13 names in all.) Old MacDonald usually starts his day by walking down to the lake to feed his ducks. This particular morning he realized the ducks were crowded around the cows’ field. This is unusual. They usually spend dinner together…not breakfast! Old MacDonald feeling a little concerned began counting the legs of all this animals. “What?” screams Old MacDonald. He normally counts 40 legs, this morning he only counts 36. “What does this mean? Am I missing a cow? Am I missing two ducks?” He begins to call them by name, “Dasher, Dancer, Prancer, Vixon, Comet, Cupid, Donner, Blitzen, Blossom, Buttercup, Bubbles, Bart, and Lisa?” However, they are farm animals they don’t know their names. His wife comes out shaking her head, “Old MacDonald, you crazy old man, what are you doing out here?” “Honey, I am missing one or two of my animals. Please help me find them” he begs. “Alright, dear. How many cows and ducks are you supposed to have?” “I have 6 ducks and 7 cows.” “Now, Old MacDonald, I see 13 animals,” laughs Mrs. MacDonald. Old MacDonald counts again and sees the same 36 legs. Just then a gust of wind blows by and the ducks go flying and lands again. Old MacDonald counted again. 40! “They came back!” he yelled. “Yes, they came back,” agreed Mrs. MacDonald. She decided to not tell him two of the ducks sat on a back of a cow. “Poor Old MacDonald.” Example System of Equations: X = cows Y = ducks Substitution: 4x+ 2y = 40 x+y = 13 -x -x y=-x+13 4x + 2(-x+13)=40 4x-2x+26 = 40 2x+26= 40 -26 -26 2x = 14 2 X = 7 (7. 6) 4x+ 2y = 40 x+y = 13 7 + y = 13 -7 -7 y = 6 Graph and Table 4x+ 2y = 40 x+y = 13 -4x -4x -x -x 2y = -4x-10 y = -x+13 2 2 Y = -2x – 5 Elimination: 4x+ 2y = 40 4x+2y=40 7 + y =12 -2(x+y = 13) -2x-2y = -26 -7 -7 2x= 14 y = 6 2 2 x = 7 (7. 6) Check: 4(7) + 2(6) = 40 28 + 12 = 40 40 = 40 6 + 7 = 13 13 = 13

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