Solving Systems of Equations with Substitution

This video tutorial explains how to solve a system of equations using the substitution method. It begins with an introduction to the method, followed by a detailed example where y is substituted, leading to the solution of x and y. Another example is provided where x is substituted, demonstrating the flexibility of the method. The video concludes by mentioning other methods like elimination and graphing, highlighting when substitution is most effective.

What is the primary goal of the substitution method?

• To find the values of x and y that satisfy both equations

• To eliminate one of the variables

• To convert all equations into standard form

• To graph the equations on a coordinate plane

What do we substitute into the other equation?

• The value of one variable from one equation into the other

• A new variable to simplify the equation

• The entire first equation

• A numerical value for x or y

After substituting y = 6 - x into the second equation, what is the next step?

• Substitute another value for x

• Combine like terms to simplify the equation

• Graph the equation to find the solution

• Solve for y directly

What is the value of x found in the first example?

• 4

• 6

• -4

• 2

How do we find the value of y after determining x in the first example?

• Subtract x from 6

• Substitute x back into the original equation

• Multiply x by 2

• Add x to 6

In the second example, what equation is used to substitute for x?

• x = 2y + 3

• x = 3y - 2

• x = -y + 3

• x = y - 3

What is the first step after substituting x in the second example?

• Solve for x immediately

• Combine like terms

• Distribute the coefficient through the parentheses

• Graph the resulting equation

What value of y is found in the second example?

• -2

• -1

• 2

• 1

After finding y, how do we find x in the second example?

• Substitute y into x = -y + 3

• Add y to 3

• Subtract y from 3

• Substitute y back into the original equation

What are the other methods mentioned for solving systems of equations?

• Graphing and elimination

• Multiplication and division

• Factorization and simplification

• Addition and subtraction