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Solve each system using Elimination.

1. 2x + 3y = 8

x – y = 2

2. x – 2y = 5

3x – 5y = 8

3. -5x + 8y = 21

10x + 3y = 15

Solving Systems of Linear Equations: Word Problems Objective: Set up a system of equations to describe a given situation, and solve using elimination or substitution

Solving Word Problems with 2 Variables

Step 1: Identify the Variables State exactly what each variable represents Ex: “Let x = # of dimes and y = # of quarters”

Step 2: Write the Equations Write two equations Each sentence/phrase will translate into an equation

Step 3: Solve the System of Equations Use elimination or substitution

Step 4: Answer the question

Step 5: Check Make sure the solution actually works Reject any inappropriate answers

Examples

Ex 1: The sum of two numbers is 18. The sum of the greater number and twice the smaller number is 25. Find the numbers.

Step 1: Identify the variables Let x = the greater number

y = the smaller numberStep 2: Write the equations:

x + y = 18x + 2y = 25

Step 3: Use substitution or elimination to solve.

Step 4: Answer the question: x = 11, the greater numbery = 7, the smaller number

Step 5: Check

Examples

Ex: Suppose a band at another school sells erasers for $2 per package and pencils for $5 per package. The band sells 220 packages in all and earns a total of $695. Write a system of equations to find the number of each type of package sold.

Step 1: Let x = packages of erasers

y = packages of pencils

Step 2: x + y = 220

2x + 5y = 695

Step 3: Solve the equations.

Step 4: Answer the question.

x = 135 packages of erasers

y = 85 packages of pencils

Step 5: Check.

Try It!On one day, the Rock and Roll Hall of Fame in Cleveland, Ohio, admitted 4400 adults and students and collected $57,200 in ticket sales. The price of admission is $14 for an adult and $10 for a student. How many adults and how many students were admitted to the museum that day?

Try It!

On one day, the American Museum of Natural History in New York City, admitted 541 adults and children and collected $9020 in ticket sales. The price of admission is $40 for an adult and $11 for a child. Find how many adults and children were admitted to the museum on that day.