Solving Systems

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 one solution?

Back

The graphs of the equations intersect at exactly one point.

Front

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

Back

The graphs of the equations are parallel and never intersect.

Front

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

Back

The graphs of the equations are the same line, overlapping completely.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

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

Back

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

Front

What are parallel lines in the context of systems of equations?

Back

Lines that have the same slope but different y-intercepts, indicating no solutions.

Front

What are intersecting lines in the context of systems of equations?

Back

Lines that cross at one point, indicating one unique solution.