Solving Systems by Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean if a system of equations has infinite solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

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

Back

Make sure at least one equation is solved for one variable.

Front

How do you determine if a solution is correct for a system of equations?

Back

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

Front

What is the graphical interpretation of a system of equations with one solution?

Back

The two lines intersect at exactly one point.

Front

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

Back

The two lines lie on top of each other, representing the same line.

Front

What is the graphical interpretation of a system of equations with no solution?

Back

The two lines are parallel and never intersect.

Front

What is the importance of isolating a variable in the substitution method?

Back

Isolating a variable allows for easier substitution into the other equation.