Solving Systems of Equations by Substitution

The video tutorial explains how to solve systems of equations using the substitution method. It begins with an introduction to the method, followed by detailed steps for implementation. Several example problems are solved to demonstrate the process, including handling special cases like no solution or infinite solutions.

Which method is not covered in this video?

• Substitution

• Graphing

• Elimination

• Matrix Method

What is the first step in the substitution method?

• Check for solutions

• Graph the equations

• Substitute the expression into the other equation

• Solve one equation for x or y

If you have y = 4x - 1 and y = 2x - 5, what should you do next?

• Graph the equations

• Set the equations equal to each other

• Add the equations

• Subtract the equations

After substituting and solving for one variable, what is the next step?

• Check for errors

• Substitute the found value back into one of the original equations

• Solve for the other variable

• Graph the solution

In the example where y = 6x and 3y = 18x - 5, what is the value of x?

• -1

• 0

• 2

• 1

What is the ordered pair solution for the system y = 6x and 3y = 18x - 5?

• (-1, -6)

• (1, 6)

• (-1, 6)

• (1, -6)

When solving a system where one equation is x = 4y + 7, what should you substitute?

• y for 4y + 7

• x for 4y + 7

• 4y + 7 for y

• 4y + 7 for x

What does it mean if you end up with a statement like 54 = 54 when solving a system?

• There is no solution

• There is one solution

• There are infinitely many solutions

• The system is inconsistent

What does it mean if you end up with a statement like 0 = 5 when solving a system?

• There is one solution

• There are infinitely many solutions

• The system is consistent

• There is no solution

If neither equation is in the form y = ... or x = ..., what should you do first?

• Graph the equations

• Solve one equation for x or y

• Check for solutions

• Add the equations