Systems of Equations

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 two lines to intersect?

Back

It means they have a common solution, or point, where they meet.

Front

What is the point of intersection?

Back

The coordinates (x, y) that satisfy both equations in a system.

Front

What does it mean if two lines are parallel?

Back

They do not intersect and have no solutions.

Front

What is a linear equation?

Back

An equation that graphs to a straight line, typically in the form y = mx + b.

Front

What is a quadratic equation?

Back

An equation that graphs to a parabola, typically in the form y = ax^2 + bx + c.

Front

How many solutions can a linear-quadratic system have?

Back

0, 1, or 2 solutions depending on the graphs' intersection.

Front

What is an infinite solution in a system of equations?

Back

When two equations represent the same line, resulting in countless intersection points.

Front

What does 'no solution' indicate in a system of equations?

Back

The lines are parallel and do not intersect.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines or curves representing the equations.