Systems of Linear Equations

Front

What is a system of linear equations?

Back

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

Front

What does it mean for two lines to intersect on a graph?

Back

It means that the system of equations has one unique solution, which is the point of intersection.

Front

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

Back

Two parallel lines that never intersect.

Front

What is the graphical representation of a system with infinitely many solutions?

Back

Two lines that lie on top of each other (coincident lines).

Front

How do you find the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

If a system of equations has one solution, what can be said about the slopes of the lines?

Back

The lines have different slopes.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if a system of equations is consistent or inconsistent?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.