IXL - Solve a system of equations using elimination: word problems (Algebra 1 practice)

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

For a project in statistics class, a pair of students decided to invest in two companies, one that produces software and one that does biotechnology research. Logan purchased 58 shares in the software company and 8 shares in the biotech firm, which cost a total of $2,120. At the same time, Mabel invested a total of $4,458 in 33 shares in the software company and 57 shares in the biotech firm. How much did each share cost?

Each share in the software company cost $, and each share in the biotech firm cost $.

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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.

An employee at a company that assembles chandeliers is packing boxes for shipping. In the first box, he packed 1 small chandelier and 2 large chandeliers, which weighed a total of 78 kilograms. In the second box, he packed 5 small chandeliers and 1 large chandelier, which had a weight of 93 kilograms. Assuming the weight of the box isn't included in the shipping weight, how much does each size of chandelier weigh?

Each small chandelier weighs kilograms and each large one weighs kilograms.

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 weight of a small chandelier, and let y represent the weight of a large chandelier.

x + 2y = 78

5x + y = 93

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 5x) nor the y terms (2y and y) are opposites. Use multiplication to rewrite the equations with either opposite x terms or opposite y terms. One good approach is to multiply the second equation by ^–2.

x + 2y = 78

→

x + 2y = 78

^–2(5x + y = 93)

→

^–10x − 2y = ^–186

Now the y terms (2y and ^–2y) are opposites.

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

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

Add to eliminate the y terms
	x	+	2y	=	78
+ (	^–10x	−	2y	=	^–186	)


	^–9x	+	0y	=	^–108	Add to eliminate the y terms

Simplify
			^–9x	=	^–108	Simplify

Divide both sides by ^–9
			x	=	12	Divide both sides by ^–9

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

Take the result of Step 2, x = 12, and plug it into one of the original equations, such as x + 2y = 78. Then find the value of y.

x + 2y

Plug in x = 12

12 + 2y

Plug in x = 12

Subtract 12 from both sides

Divide both sides by 2

Step 4: State the solution.

Since x = 12 and y = 33, the solution is (12, 33).

Each small chandelier weighs 12 kilograms and each large one weighs 33 kilograms.

Looking for more? Try these:

Lesson: Systems of equations

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Not feeling ready yet? These can help:

O.10Solve a system of equations using elimination

N.8Write a linear function: word problems

C.9Solve one-step and two-step linear equations: word problems

Lesson: Systems of equations

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