Solving Systems of Equations Using Substitution

Nancy explains how to solve systems of linear equations using the substitution method. She provides a step-by-step guide, including special cases like infinite solutions and no solution. The video concludes with additional examples and encourages viewers to practice the method.

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

• Multiply both equations by a common factor

• Add the equations together

• Graph the equations

• Solve for y or x in either equation

After isolating a variable in one equation, what should you do next?

• Divide both sides by the isolated variable

• Isolate the same variable in the other equation

• Substitute the isolated variable into the other equation

• Add the isolated variable to both sides of the equation

In the example provided, what value is found for x after solving the first equation?

• 3

• 5

• 2

• 7

What is the final solution for the system of equations in the simple example?

• (3, 5)

• (2, 7)

• (0, 6)

• (1, 4)

When dealing with fractions in a system of equations, what is a helpful way to handle the multiplication?

• Add the fractions together first

• Ignore the fractions and solve directly

• Convert all fractions to decimals

• Multiply the fractions straight across

What does it mean if you end up with a statement like -8 = -8 when solving a system of equations?

• The system is inconsistent

• There is one unique solution

• There are infinitely many solutions

• There is no solution

What does it mean if you end up with a statement like -8 = 4 when solving a system of equations?

• There is no solution

• There is one unique solution

• There are infinitely many solutions

• The system is consistent

If one of the equations in a system is already in the form y = or x =, what should you do?

• Ignore that equation

• Rearrange it to a different form

• Use it to substitute into the other equation

• Solve it separately

What should you do if both equations in a system start with y =?

• Set the right sides of the equations equal to each other

• Panic and give up

• Add the equations together

• Multiply both equations by a common factor

What is the main focus of this video tutorial?

• Matrix method

• Substitution method

• Graphing method

• Elimination method