Solving Systems of Equations by Substitution

This video tutorial covers solving systems of equations using the substitution method. It begins with an introduction to the method, explaining how to replace variables in one equation with expressions from another. The tutorial includes examples of different scenarios, such as when one equation is already solved for a variable, when equations are in standard form, and when both equations are solved for the same variable. Special cases, like infinite solutions and no solutions, are also discussed. The video aims to provide a comprehensive understanding of the substitution method and its application in solving systems of equations.

What does substitution in systems of equations involve?

• Replacing a variable with its equivalent expression from another equation

• Replacing a variable with another variable

• Graphing two equations to find their intersection

• Solving each equation separately without considering the other

When solving by substitution, what do you do if one equation is already solved for a variable?

• Solve the equation as is without substitution

• Graph the equation

• Substitute the expression for the variable into the other equation

• Rearrange the equation to solve for the other variable

What does a solution of a system of equations represent graphically?

• The point where the two graphs touch

• The area shared by the two graphs

• The x-intercepts of both graphs

• The y-intercepts of both graphs

What is the result when the graphs of two equations are the same line?

• Infinitely many solutions

• Exactly two solutions

• Exactly one solution

• No solution

What does it mean if after substitution, you get a true statement like 5=5?

• The system has infinitely many solutions

• The system has exactly one solution

• The system has no solution

• The system has exactly two solutions

In a system of equations, if substituting one equation into the other results in a variable canceling out and leaving a true statement, what does it indicate?

• The system has no solution

• The equations are unrelated

• The system has exactly one solution

• The system has infinitely many solutions

How can you solve a system of equations if neither equation is initially set equal to a variable?

• By substituting numbers for variables

• By manipulating one equation to isolate a variable

• By adding both equations directly

• By graphing both equations

What is the first step in solving a system of equations by substitution when neither equation is set equal to a variable?

• Graph both equations

• Combine both equations

• Isolate a variable in one of the equations

• Substitute arbitrary values for variables

What is the solution to a system of equations if after substitution, you get a false statement like 5=-5?

• Infinitely many solutions

• No solution

• Exactly one solution

• Exactly two solutions

If both equations in a system are set equal to the same variable, how do you find the solution?

• By graphing the equations

• By setting the expressions equal to each other

• By adding the equations together

• By substituting values from one equation into the other