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## 7.2 The Substitution Method

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**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.**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.**Ex. 1 Solve by using substitution: b.**• 2x – 4 (2) = 1 • 2x – 8 = 1 • 2x = 9 • X = 4.5 • (4.5, 2)**Ex. 2a.**• 4x + 5 (4x) = -24 • 4x + 20x = -24 • 24x = -24 • X = -1 • Y = 4 (-1) • Y = -4 • Solution is (-1, -4)**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)**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