Flashcard: Systems by Graphing & Substitution

Front

What does it mean if a system of linear equations has one solution?

Back

The two lines intersect at exactly one point.

Front

What does it indicate if a system of linear equations has infinitely many solutions?

Back

The two lines are coincident, meaning they lie on top of each other.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the graphical representation of a system with no solutions?

Back

The two lines are parallel and never intersect.

Front

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

Back

Look for an equation in the form y=_______ or x=__________.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What does it mean if two lines in a system have the same slope but different y-intercepts?

Back

The system has no solutions because the lines are parallel.

Front

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

Back

It represents the solution to the system, where both equations are satisfied.

Front

How can you verify the solution of a system of equations?

Back

By substituting the solution back into both original equations to check for validity.

Front

What is the difference between consistent and inconsistent systems of equations?

Back

Consistent systems have at least one solution, while inconsistent systems have no solutions.