Solve System by Substitution

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of both variables.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable on one side of the equation by itself.

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution, meaning their graphs intersect at one or more points.

Front

What is an inconsistent system of equations?

Back

An inconsistent system of equations has no solution, meaning the lines represented by the equations are parallel and never intersect.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

How can you check your solution after solving a system of equations?

Back

You can check your solution by substituting the values of the variables back into the original equations to see if they hold true.

Front

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

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the solution to the system, indicating the values of the variables that satisfy both equations.

Front

How do you handle a system of equations with no solution?

Back

If a system of equations has no solution, you can conclude that the equations represent parallel lines.

Front

What is the difference between dependent and independent systems of equations?

Back

Dependent systems have infinitely many solutions (the equations represent the same line), while independent systems have exactly one solution (the lines intersect at one point).