Solving A System of Equations

Solving A System of Equations Ana Garcia Emily Gonzalez December 18, 2013 7/8 pD

Problem Situation • A basketball team stopped at a fast food restaurant after a game. They divided into two groups. • One group bought 5 chicken sandwiches and 7 hamburgers for a cost of $24.90. • The second group spent $28.80 and bought 5 chicken sandwiches and 9 hamburgers. • How much does a hamburger cost?

Define Variables • H represents the cost of one hamburger • C represents the cost of one chicken sandwich

System of Equations 5C + 7H = 24.90 5C + 9H = 28.80

Solution Method • The system of equations is going to solved by the method of elimination. • The variable c is going to be eliminated when we subtract the equations.

Step _1_ of Solution We eliminate the 5C 5C + 7H = 24.90 5C + 9H = 28.80 ------------------------------- 2H = 3.90

Step _2_ of solution • You divide 3.90 by 2 2H = 3.90 H = 3.90 / 2 = 1.95

Step _3_ of solution • Use either equation to find C 5C + 7H = 24.90 5C + 7(1.95) = 24.90 5C + 13.65 = 24.90 5C = 11.25 C = 2.25

Solution to the System of Equations The solution to the system of equations is (2.25,1.95)

Check of Solution • 5(2.25)+7(1.95)=24.90 true • 5(2.25)+9(1.95)=28.80 true ----------------------------

Solution in the Problem Situation Each chicken sandwich is $2.25 and each hamburger is $1.95

Solving A System of Equations