Solving Systems of Equations

This video tutorial covers solving word problems using systems of equations. It begins with an introduction to key vocabulary terms, followed by a step-by-step guide on translating word problems into systems of equations. The tutorial includes four examples: a number problem, a school problem, a money problem, and a shopping problem, each demonstrating different methods like substitution and elimination. The lesson concludes with exercises for students to practice independently.

What is a system of equations?

• A single equation with multiple variables

• Two or more equations that are related to the same problem

• A set of equations that have no solution

• An equation with only one solution

What is the first step in solving word problems using systems of equations?

• Translate the problem into equations

• Solve the equations

• Read the problem carefully

• Guess the solution

In Example 1, what method is used to solve the system of equations?

• Trial and error method

• Elimination method

• Substitution method

• Graphing method

In Example 1, what are the two numbers if their sum is 361 and their difference is 173?

• 267 and 94

• 300 and 61

• 250 and 111

• 200 and 161

In Example 2, what is the relationship between the number of girls and boys?

• The number of girls is equal to the number of boys

• The number of girls is half the number of boys

• 34 more than four times the number of girls is equal to half the number of boys

• The number of boys is twice the number of girls

In Example 2, how many boys are there if there are 32 girls?

• 356

• 150

• 200

• 324

In Example 3, how many five-dollar bills does the family member have if they have 18 bills totaling $62?

• 13

• 5

• 7

• 11

In Example 4, what is the cost of seven notebooks if two boxes of pencils and eight notebooks cost $11?

• $10.00

• $7.00

• $6.50

• $5.25

Which method is used in Example 3 to solve the system of equations?

• Graphing method

• Substitution method

• Elimination method

• Trial and error method

In Example 4, what is the main focus of the problem?

• Finding the total cost of all items

• Finding the cost of pencils

• Finding the cost of notebooks

• Finding the total number of items