Exploring Rational Expressions in Algebra

The video tutorial covers solving linear systems using the substitution method. It begins with an introduction to the concept, followed by a detailed explanation of the substitution method. The tutorial includes step-by-step solutions to example problems and discusses special cases such as no solution and infinite solutions. Finally, it applies the substitution method to a word problem, demonstrating its real-world application.

What happens when two lines in a linear system are parallel?

• They form a right angle.

• They intersect at one point.

• They have no solution.

• They have infinitely many solutions.

In the substitution method, what should you look for to avoid fractions?

• A variable with a coefficient of 0

• A variable with a coefficient of 2

• A variable with a coefficient of 1

• A variable with a negative coefficient

What is the first step in solving a system using substitution?

• Graphing the equations

• Isolating one of the variables

• Multiplying both equations

• Adding the equations together

What should you do after finding the x-value in a system of equations?

• Graph the equations

• Add the equations together

• Substitute it back to find the y-value

• Multiply both equations

What is the final step in verifying the solution of a system of equations?

• Adding the solution to both equations

• Multiplying the solution by a constant

• Checking the solution in both original equations

• Graphing the solution

What should you do if you encounter fractions while isolating a variable?

• Divide both sides by a constant

• Try to avoid them if possible

• Ignore them

• Multiply both sides by a constant

What does it mean if you get a true statement like -28 = -28 when solving a system?

• The system is inconsistent.

• There are infinitely many solutions.

• There is exactly one solution.

• There is no solution.

What does it mean if you get a false statement like -24 = 18 when solving a system?

• The system is dependent.

• There are infinitely many solutions.

• There is exactly one solution.

• There is no solution.

In the word problem involving boats, what does 8.5 represent?

• The distance between the boats

• The speed of the second boat

• The speed of the first boat

• The time it takes for the second boat to catch up

How do you find the distance the boats are from their port after 8.5 hours?

• By adding the speeds of both boats

• By multiplying the speed of one boat by 8.5

• By dividing the speed of one boat by 8.5

• By subtracting the speeds of both boats