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) = 12x – 8 = 12x = 9X = 4.5(4.5, 2)

Ex. 2a.4x + 5 (4x) = -244x + 20x = -2424x = -24X = -1

Y = 4 (-1)Y = -4Solution 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) = 375050n + 200n + 1000 = 3750250n = 2750N = 11 last year’s T-shirt11 + 5 = MM = 16 for this year’s T-shirt