Solving A System of Equations

Solving A System of Equations Julio Munoz & Oscar Acosta December 19, 2013 2-3B

Problem Situation • Lamar wants to spend $32 on fish at Fin City. He can buy 4 large goldfish and 4 guppies or he can buy 1 large goldfish and 9 guppies. • What is the cost of each breed of fish?

Define Variables • G = cost of goldfish • P = cost of guppies

System of Equations • 4G + 4P = 32 • 1G + 9P =32

Solution Method • To find the solution to our problem we used substitution.

Step 1 of Solution • We solved for G: 1G + 9P =32 G = 32 – 9P • We can now substitute what G equals into the other equation.

Step 2 of Solution • 4G + 4P = 32 • 4(32-9P) + 4P = 32 Substitute 32 – 9P for G • 128 + -36P + 4P = 32 Use the distributive property • 128 + -32P = 32 Combine like terms • -32P = -96 Subtract 128 from both sides P = 3 Divide both sides by -32

Step 3 of Solution • Remember that 1G + 9P =32 G = 32 – 9P • G = 32 – 9(3) Substitute 3 for P • G = 32 – 27 Multiply • G = 5 Simplify by subtracting

Solution to the System of Equations • P = 3 • G = 5 (5,3) is a solution to the system.

Check of Solution 4(5) + 4(3) = 32 1(5) + 9(3) = 32

Solution in the Problem Situation • $5 is the cost for goldfish. • $3 is the cost for guppies.

Solving A System of Equations