Exploring Rational Expressions: Addition and Subtraction Techniques

The video tutorial covers solving systems of linear equations derived from word problems. It includes examples such as determining the number of correct and incorrect answers in a test, finding two numbers based on their sum and difference, and calculating the speed of a boat in still water and current. The tutorial emphasizes the elimination method and provides step-by-step guidance for each problem.

What type of equations are we focusing on in this section?

• Quadratic equations

• Polynomial equations

• Exponential equations

• Linear equations

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

• Solving the equations

• Defining what x and y represent

• Graphing the equations

• Checking the solutions

If a student answers 100 questions and receives 170 points, how many questions did they answer correctly?

• 95

• 90

• 85

• 80

Given that the total number of questions is 100 and the number of correct answers is 90, how many questions were answered incorrectly?

• 20

• 15

• 10

• 5

If the difference between two numbers is 3 and their sum is 13, what are the two numbers?

• 6 and 7

• 5 and 8

• 3 and 10

• 4 and 9

What is the sum of the two numbers if their difference is 3 and one of the numbers is 8?

• 10

• 11

• 12

• 13

When a boat travels upstream, what is the relationship between the boat's speed and the current?

• The boat's speed is added to the current

• The boat's speed is subtracted from the current

• The boat's speed is multiplied by the current

• The boat's speed is divided by the current

If a boat travels 210 miles downstream in 10 hours, what is the effective speed of the boat downstream?

• 10 miles per hour

• 21 miles per hour

• 15 miles per hour

• 20 miles per hour

What is the rate of the boat in still water if it travels upstream at 3 miles per hour and downstream at 21 miles per hour?

• 15 miles per hour

• 12 miles per hour

• 18 miles per hour

• 9 miles per hour

If the rate of the current is 9 miles per hour, what is the rate of the boat in still water?

• 3 miles per hour

• 15 miles per hour

• 12 miles per hour

• 6 miles per hour