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Solving systems of equations with 2 variables Word problems (Number Problems)

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1) The sum of two numbers is 72. Their difference is 40. Find the numbers. The sum of two numbers is 72. x + y = 72 Their difference is 40. x – y = 40

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1) The sum of two numbers is 72. Their difference is 40. Find the numbers. x + y = 72 x – y = 40 Which method should be used to solve this system of equations? a) Substitution Method b) Elimination (Addition) Method

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1) The sum of two numbers is 72. Their difference is 40. Find the numbers. Solve using the Elimination (Addition) Method x + y = 72 x – y = 40 2x = 112 x = 56 Back substitute 56 + y = 72 56 + y + (-56) = 72 + (-56) y = 16 The numbers are 56 and 16.

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2) The sum of two numbers is 21. Their difference is 13. Find the numbers. Solve using the Elimination (Addition) Method x + y = 21 x – y = 13 2x = 34 x = 17 Back substitute 17 + y = 21 17 + y + (-17) = 21 + (-17) y = 4 The numbers are 17 and 4.

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3) The sum of two numbers is 27. One number is three more than the other. Find the numbers. The sum of two numbers is 27. x + y = 27 One number is 3 more than the other. y = x + 3

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3) The sum of two numbers is 27. One number is three more than the other. Find the numbers. x + y = 27 y = x + 3 Which method should be used to solve this system of equations? a) Substitution Method b) Elimination (Addition) Method

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Solve using the Substitution Method x + y = 27 y = x + 3 x + (x + 3) = 27 2x + 3 = 27 2x + 3 + (-3) = 27 + (-3) 2x = 24 x = 12 3) The sum of two numbers is 27. One number is three more than the other. Find the numbers. Back substitution y = x + 3 y = 12 + 3 y = 15 The numbers are 12 and 15.

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Solve using the Substitution Method x + y = 36 y = 3x x + (3x) = 36 4x = 36 x = 9 4) A 36-ft rope is cut into two pieces. One piece is three times the other. Find the length of each piece. Back substitution y = 3x y = 3(9) y = 27 The pieces are 9 ft and 27 ft.

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Solve using the Substitution Method L – S = 3 L = 2S + 1 (2S + 1) – S = 3 S + 1 = 3 S + 1 + (-1) = 3 + (-1) S = 2 5) The difference between two numbers is 3. The larger number is one more than twice the smaller number. Find the numbers. Back substitution L = 2S + 1 L = 2(2) + 1 L = 5 The numbers are 2 and 5.

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