Substitution Method for Solving Systems of Equations

This video tutorial explains the substitution method for solving systems of equations. It covers the steps to isolate a variable, substitute it into another equation, and solve for the remaining variable. The video includes examples demonstrating one solution, no solution, and infinite solutions, with graphical verification using a calculator.

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

• Check the solution

• Multiply both equations by a constant

• Graph the equations

• Solve for a variable in one of the equations

In the substitution method, after substituting the isolated variable into the other equation, what should you obtain?

• A solution set

• An equation with one variable

• A graph of the equation

• An equation with two variables

How can you verify the solution obtained from the substitution method?

• By substituting the values back into the original equations

• By multiplying the solution by a constant

• By adding the solution to another equation

• By ignoring the solution

What does it mean graphically if two lines intersect at a point?

• The lines are parallel

• There is no solution

• There is one solution

• There are infinite solutions

What indicates that a system of equations has no solution when using the substitution method?

• The solution is a fraction

• The solution is a negative number

• The variables simplify to zero and the statement is true

• The variables simplify to zero and the statement is false

What is the graphical representation of a system with no solution?

• Intersecting lines

• Parallel lines

• Overlapping lines

• A single line

If the substitution method results in a true statement after variables simplify to zero, what does this indicate?

• The solution is incorrect

• There are infinite solutions

• There is one solution

• There is no solution

What is the graphical interpretation of a system with infinite solutions?

• A single point

• Intersecting lines

• Parallel lines

• Overlapping lines

In the substitution method, what should you do if the resulting equation is a contradiction?

• Assume there are infinite solutions

• Recalculate the substitution

• Conclude there is no solution

• Assume there is one solution

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

• Graph the solution

• Check the solution

• Add the solution to another equation

• Multiply the solution by a constant