Master solving a system of equations by substitution with no solution and infinite many

The video tutorial explains how to solve systems of equations using substitution, focusing on cases with no solutions and infinite solutions. It covers identifying variables with coefficients of 1 or -1 for substitution, solving algebraically, and understanding the graphical representation of solutions. The tutorial demonstrates solving systems with no solutions, where lines are parallel, and systems with infinite solutions, where lines overlap.

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

• Identify the variable with a coefficient of 1 or -1

• Graph the equations

• Eliminate one of the variables

• Identify the variable with the largest coefficient

When solving a system of equations, what does it mean if you end up with a statement like -14 = 7?

• The system is inconsistent

• The system has exactly one solution

• The system has no solutions

• The system has infinite solutions

In the context of solving systems of equations, what does it mean if two lines are parallel?

• They are the same line

• They have the same slope but different y-intercepts

• They intersect at one point

• They have different slopes

What is the result when you solve a system of equations and find that 15 = 15?

• The system has no solutions

• The system has infinite solutions

• The system has exactly one solution

• The system is inconsistent

How can you verify that a system of equations has infinite solutions?

• By checking if the equations have different slopes

• By checking if the equations have the same slope and y-intercept

• By checking if the equations have the same slope but different y-intercepts

• By checking if the equations have different y-intercepts

What is the significance of a variable having a coefficient of 1 or -1 in substitution?

• It means the variable should be eliminated

• It indicates the variable is not part of the solution

• It makes the variable easier to solve for

• It shows the variable is dependent

What is the main difference between systems with no solutions and systems with infinite solutions?

• No solutions have different slopes, infinite solutions have the same slope

• No solutions have the same slope, infinite solutions have different slopes

• No solutions have different y-intercepts, infinite solutions have the same y-intercept

• No solutions have the same slope but different y-intercepts, infinite solutions have the same slope and y-intercept