IXL | Solve a system of equations using elimination: word problems

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

Deion had brochures printed for his new business venture. He originally ordered 5 boxes of black-and-white brochures and 4 boxes of color brochures, which cost a total of $146. After those ran out, he spent $122 on 5 boxes of black-and-white brochures and 3 boxes of color brochures. Given that the prices didn't change, what was the price of each type of brochure?

The prices were $ for a box of black-and-white brochures and $ for a box of color brochures.

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Learn with an example

question

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

The drama club is selling gift baskets to raise money for new costumes. During the fall play, they sold a combined 1 regular gift basket and 15 deluxe gift baskets, earning a total of $695. During the spring musical, they sold 19 regular gift baskets and 17 deluxe gift baskets, earning a total of $1,145. How much are they charging for the different sized gift baskets?

The drama club is charging $ for a regular gift basket and $ for a deluxe gift basket.

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 amount charged for a regular gift basket, and let y represent the amount charged for a deluxe gift basket.

x + 15y = 695

19x + 17y = 1,145

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 19x) nor the y terms (15y and 17y) 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 ^–19.

^–19(x + 15y = 695)

→

^–19x − 285y = ^–13,205

19x + 17y = 1,145

→

19x + 17y = 1,145

Now the x terms (^–19x and 19x) 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
	^–19x	−	285y	=	^–13,205
+ (	19x	+	17y	=	1,145	)


	0x	−	268y	=	^–12,060	Add to eliminate the x terms

Simplify
			^–268y	=	^–12,060	Simplify

Divide both sides by ^–268
			y	=	45	Divide both sides by ^–268

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

Take the result of Step 2, y = 45, and plug it into one of the original equations, such as x + 15y = 695. Then find the value of x.

x + 15y

695

Plug in y = 45

x + 15(45)

695

Plug in y = 45

Multiply

x + 675

695

Multiply

Subtract 675 from both sides

Step 4: State the solution.

Since x = 20 and y = 45, the solution is (20, 45).

The drama club is charging $20 for a regular gift basket and $45 for a deluxe gift basket.

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Lesson: Systems of equations

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Lesson: Systems of equations

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