Solving Linear Equations and Systems

This video tutorial covers solving linear systems using the substitution method. It begins with an introduction to substitution, followed by exercises on isolating variables. The tutorial then demonstrates solving linear systems step-by-step, including checking solutions by substituting back into the original equations. Special cases, such as no solution or infinite solutions, are also discussed.

What is the first step in solving linear systems using substitution?

• Multiplying the equations

• Graphing the equations

• Isolating a variable

• Adding the equations

When isolating x in the equation x + 3y = 8, what is the correct expression for x?

• x = 8 + 3y

• x = 8 - 3y

• x = 3y - 8

• x = 3y + 8

In the equation -x + 7y = 0, what is the correct expression for x?

• x = 0

• x = -7y

• x = y

• x = 7y

What is the result of isolating y in the equation 2x - y = 3?

• y = 2x + 3

• y = 2x - 3

• y = 3 - 2x

• y = 3 + 2x

What does substitution involve in solving linear systems?

• Adding two equations

• Graphing the equations

• Eliminating a variable

• Replacing one variable with another

In the substitution method, what should you do after finding the value of one variable?

• Find the value of the other variable

• Graph the solution

• Check the solution

• Stop the process

What is the solution to the system of equations x + 4y = 6 and 2x - 3y = 1?

• (2, 1)

• (1, 2)

• (0, 0)

• (3, 2)

What happens when you get 0 = 0 while solving a system of equations?

• There is no solution

• The solution is incorrect

• There is one solution

• There are infinite solutions

What does it mean if two lines have the same slope but different y-intercepts?

• They have no slope

• They intersect at one point

• They are parallel

• They are the same line

What is the result when two equations represent the same line?

• Infinite solutions

• One solution

• No solution

• Incorrect solution