IXL - Solve a system of equations using elimination: word problems (Precalculus practice)

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

Sparkles the Clown makes balloon animals for children at birthday parties. At Jamie's party, he made 1 balloon poodle and 1 balloon giraffe, which used a total of 5 balloons. For Helen's party, he used 16 balloons to make 2 balloon poodles and 4 balloon giraffes. How many balloons does each animal require?

Each poodle requires balloons and each giraffe requires balloons.

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question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

Parent volunteers at Castroville High School are processing yearbook order forms. Students have an option to get the basic yearbook or a deluxe option, which includes engraving and a protective cover. In Mrs. Burton's class, 1 basic yearbook and 15 deluxe yearbooks were ordered, for a total of $1,441. The students in Mr. Long's class ordered 6 basic yearbooks and 18 deluxe yearbooks, for a total of $2,094. How much does each option cost?

The basic yearbook costs $, and the deluxe yearbook costs $.

key idea

To solve using elimination, follow these four steps:

Step 1: Make sure the equations have opposite x terms or opposite y terms.

Step 2: Add to eliminate one variable and solve for the other.

Step 3: Plug the result of Step 2 into one of the original equations and solve.

Step 4: State the solution.

solution

Before you can solve, you must write a system of equations. Let x represent the cost of a basic yearbook, and let y represent the cost of a deluxe yearbook.

x + 15y = 1,441

6x + 18y = 2,094

Now use elimination to solve the system of equations.

Step 1: Make sure the equations have opposite x terms or opposite y terms.

Currently, neither the x terms (x and 6x) nor the y terms (15y and 18y) are opposites. Use multiplication to rewrite the equations with either opposite x terms or opposite y terms. One good approach is to multiply the first equation by ^–6.

^–6(x + 15y = 1,441)

→

^–6x − 90y = ^–8,646

6x + 18y = 2,094

→

6x + 18y = 2,094

Now the x terms (^–6x and 6x) are opposites.

Step 2: Add to eliminate one variable and solve for the other.

Add to eliminate the x terms, and then solve for y.

Add to eliminate the x terms
	^–6x	−	90y	=	^–8,646
+ (	6x	+	18y	=	2,094	)


	0x	−	72y	=	^–6,552	Add to eliminate the x terms

Simplify
			^–72y	=	^–6,552	Simplify

Divide both sides by ^–72
			y	=	91	Divide both sides by ^–72

Step 3: Plug the result of Step 2 into one of the original equations and solve.

Take the result of Step 2, y = 91, and plug it into one of the original equations, such as x + 15y = 1,441. Then find the value of x.

x + 15y

1,441

Plug in y = 91

x + 15(91)

1,441

Plug in y = 91

Multiply

x + 1,365

1,441

Multiply

Subtract 1,365 from both sides

Step 4: State the solution.

Since x = 76 and y = 91, the solution is (76, 91).

The basic yearbook costs $76, and the deluxe yearbook costs $91.

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Lesson: Systems of equations

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