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# 7.2 The Substitution Method

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1. 7.2 The Substitution Method Objective: Find an exact solution to a system of linear equations by using the substitution method. Standard Addressed: 2.8.8.E: Select an use a strategy to solve equations.

2. If you know the value of one variable in a system of equations, you can find the solution for the system by substituting the known value of the variable into one of the equations. This method is called substitution.

3. Ex. 1 Solve by using substitution: b. • 2x – 4 (2) = 1 • 2x – 8 = 1 • 2x = 9 • X = 4.5 • (4.5, 2)

4. Ex. 2a. • 4x + 5 (4x) = -24 • 4x + 20x = -24 • 24x = -24 • X = -1 • Y = 4 (-1) • Y = -4 • Solution is (-1, -4)

5. Ex. 3 b. Solve by substitution. • Solve first EQ for X  x = -6y + 1 • Substitute above EQ into the 2nd EQ • 3(-6y + 1) - 10y = 31 • -18y + 3 – 10y = 31 • -28 y + 3 = 31 • -28y = 28 • Y = -1 • Find X by substituting y = -1 into one of your above EQ. • X = -6 (-1) + 1 • X = 7 • Solution is (7, -1)

6. b. Sam sells T-shirts at a baseball park. He has 50 of last year’s T-shirts and 200 of this year’s T-shirts in stock. He knows that his customers will pay \$5 more for this year’s T-shirt. He needs to make a total of \$3750 from T-shirt sales. How much should he charge for each type? • 50N + 200m = 3750 and m = n + 5 50n + 200(n + 5) = 3750 50n + 200n + 1000 = 3750 250n = 2750 N = 11 last year’s T-shirt 11 + 5 = M M = 16 for this year’s T-shirt