# Chapter 3 - Linear Systems - 3-2 Solving Systems Algebraically - Lesson Check - Page 145: 9

2 large coffees and 3 regular coffees.

#### Work Step by Step

Form two equations using the information given. Let $x=$ number of regular coffees $y=$ number of large coffees. There are a total of five coffees purchased so: $x + y = 5$ (Equation 1) A regular coffee cost 1 dollar while a large costs 1.5 dollars. The total cost is 6 dollars therefore the equation that represents these is: $(1)x + 1.5y = 6$ $\\x + 1.5y=6$ (Equation 2) The system is: $x+y=5$ (Equation 1) $\\x+1.5y=6$ (Equation 2) Subtract Equation 1 to Equation 2 so $x$'s are eliminated: $x + 1.5y - (x + y) = 6 - (5) \\0.5y = 1$ Multiply both sides by 2. $0.5y(2) = 1(2)$ $y = 2$ Substitute $y = 2$ back into $x + y = 5$ $x + (2) = 5$ Solve by subtracting 2 from each side $x + 2 - 2 = 5 - 2$ $x = 3$ Therefore they bought 2 large coffees and 3 regular coffees.

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