Flashcardizz: 4.6 Solving by Substitution

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What does it mean if, after using substitution, the variables cancel out and you get a false statement like 5 = 2?

Back

It means there are no solutions to the system of equations.

Front

What should you do first when solving a system of equations by substitution?

Back

Solve one equation for one of the variables.

Front

What is the result of substituting a variable into an equation?

Back

You replace the variable with its equivalent expression from another equation.

Front

What does it indicate if you get a true statement like 0 = 0 after substitution?

Back

It indicates that there are infinite solutions to the system of equations.

Front

How do you check if your solution to a system of equations is correct?

Back

Substitute the solution back into both original equations to see if they hold true.

Front

What is the first step in solving the equation x² - 4x + 7 = x + 1 by substitution?

Back

Rearrange the equation to isolate one variable.

Front

What is the importance of graphing equations when solving systems?

Back

Graphing helps visualize the solutions and understand the relationship between the equations.

Front

What does it mean if two lines on a graph are parallel?

Back

It means the system of equations has no solutions.

Front

What is a common mistake when using substitution?

Back

Forgetting to substitute correctly or miscalculating after substitution.