Systems of equations and inequalities

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have a unique solution?

Back

It means the lines represented by the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means the lines represented by the equations are the same line.

Front

How can you solve a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) of intersection.

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.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.