Solving Systems of Equations with Substitution

This video tutorial introduces the substitution method for solving systems of equations, a technique students will encounter in high school. The instructor reviews previously learned methods, such as graphing and the equal values method, before explaining substitution. Through examples, the video demonstrates how to apply substitution to solve systems, including cases with no solutions. The tutorial concludes with a review and encourages students to revisit examples if needed.

What are the methods previously used to solve systems of equations?

• Substitution and elimination

• Graphing and the equal values method

• Matrix and determinant

• Integration and differentiation

What is the main advantage of using the substitution method?

• It is only useful for linear equations

• It can only be used with equal values method

• It simplifies equations to avoid fractions

• It always requires graphing

Why is substitution a preferred method when one equation is already solved for one variable?

• It avoids the use of fractions

• It directly gives the solution without any steps

• It makes it easier to substitute and solve for the other variable

• It requires less computation

In the first example, what is the value of x found using substitution?

• 11

• -11

• 4

• 0

What is the result of combining like terms in the first example?

• -2x - 35 = -13

• 2x + 35 = 13

• -5x - 35 = -13

• 5x + 35 = 13

What step follows after substituting y in the equation 5y + 3x = -13?

• Combining like terms

• Graphing the equation

• Distributing the coefficient

• Solving for x directly

What does it mean if a system of equations has no solution?

• The lines intersect at one point

• The lines intersect at multiple points

• The lines are coincident

• The lines are parallel

How do you know when a system of equations is parallel?

• When they intersect at one point

• When they have the same slope but different y-intercepts

• When they have different slopes

• When they intersect at multiple points

In the second example, what is the final value of y?

• -3

• 1

• -1

• 3

After finding the x value in the second example, what should you do next?

• Graph the equation to find y

• Substitute x back into the original equation to find y

• There is no need to find y

• Use the equal values method to find y