Solving Systems of Equations by Substitution

Mrs. Stewart introduces the substitution method for solving systems of equations, highlighting its advantages over graphing, especially when dealing with non-integer solutions or imperfect graphs. She provides a detailed explanation and examples, demonstrating how to choose variables and avoid fractions. The video concludes with encouragement to practice and a reminder to check out related videos.

Why might the graphing method not always be the most efficient way to solve systems of equations?

• It always gives incorrect solutions.

• It can only be used for linear equations.

• It requires a lot of time to draw graphs.

• Human error and non-integer solutions can make it difficult to find the exact intersection point.

What is the main advantage of the substitution method over the graphing method?

• It is faster.

• It avoids human error and non-integer solutions.

• It can be used for any type of equation.

• It always gives the correct solution.

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

• Graph the equations.

• Solve one of the equations for one of the variables.

• Combine the equations.

• Check the solution in both equations.

In the substitution method, after solving one equation for a variable, what is the next step?

• Substitute the expression into the other equation.

• Check the solution in both equations.

• Combine the equations.

• Graph the solution.

What is the final step after finding the value of one variable in the substitution method?

• Check the solution in both equations.

• Combine the equations.

• Substitute it back into the original equation to find the other variable.

• Graph the solution.

When solving a system of equations, why might you choose a variable with a coefficient of one?

• It simplifies the final answer.

• It avoids working with fractions.

• It makes the graph easier to draw.

• It always gives the correct solution.

Why is it important to check the solution in both equations?

• To ensure the solution satisfies both equations.

• To simplify the final answer.

• To avoid working with fractions.

• To make the graph easier to draw.

What should you do if all variables in the system of equations have coefficients other than one?

• Choose the variable with the largest coefficient.

• Choose the variable with the smallest coefficient.

• Choose the variable that results in the simplest fractions.

• Choose any variable randomly.

What is the main challenge when working with fractions in the substitution method?

• It requires more steps and calculations.

• It always leads to incorrect solutions.

• It makes graphing impossible.

• It only works for certain types of equations.

In the final example, what was the best option to avoid fractions?

• Choosing the variable with the largest coefficient.

• Choosing the variable that divides evenly by the other coefficients.

• Choosing the variable that results in the simplest fractions.

• Choosing the variable with the smallest coefficient.