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.

A charitable organization in Riverside is hosting a black tie benefit. Yesterday, the organization sold 30 regular tickets and 72 VIP tickets, raising $11,298. Today, 71 regular tickets and 86 VIP tickets were sold, bringing in a total of $15,851. How much do the different ticket types cost?

A regular ticket costs $, and a VIP ticket costs $.

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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.

Mario's Pizza just received two big orders from customers throwing parties. The first customer, Justin, bought 5 regular pizzas and 4 deluxe pizzas and paid $136. The second customer, Anna, ordered 5 regular pizzas and 6 deluxe pizzas, paying a total of $174. What is the price of each pizza?

Each regular pizza costs $, and each deluxe pizza 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 price of a regular pizza, and let y represent the price of a deluxe pizza.

5x + 4y = 136

5x + 6y = 174

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 (5x and 5x) nor the y terms (4y and 6y) 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 ^–1.

^–(5x + 4y = 136)

→

^–5x − 4y = ^–136

5x + 6y = 174

→

5x + 6y = 174

Now the x terms (^–5x and 5x) 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
	^–5x	−	4y	=	^–136
+ (	5x	+	6y	=	174	)


	0x	+	2y	=	38	Add to eliminate the x terms

Simplify
			2y	=	38	Simplify

Divide both sides by 2
			y	=	19	Divide both sides by 2

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

Take the result of Step 2, y = 19, and plug it into one of the original equations, such as 5x + 4y = 136. Then find the value of x.

5x + 4y

136

Plug in y = 19

5x + 4(19)

136

Plug in y = 19

Multiply

5x + 76

136

Multiply

Subtract 76 from both sides

Divide both sides by 5

Step 4: State the solution.

Since x = 12 and y = 19, the solution is (12, 19).

Each regular pizza costs $12, and each deluxe pizza costs $19.

Looking for more? Try these:

Lesson: Systems of equations

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Lesson: Systems of equations

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