Classifying Systems of Equations (12/9)

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 type of lines represent a system of equations with no solution?

Back

Parallel lines.

Front

How can you determine if a system of equations has infinitely many solutions?

Back

The equations represent the same line, meaning they overlap completely.

Front

What is the graphical representation of a system of equations with one solution?

Back

Two intersecting lines.

Front

What does it mean if two lines are parallel in the context of systems of equations?

Back

They have no points in common, hence no solution.

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

What is the elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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 is the slope-intercept form of a linear equation?

Back

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