Solve Systems of Equations - Graphing

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 solution?

Back

It means there is at least one set of values for the variables that satisfies all equations in the system.

Front

What does the graph of intersecting lines represent?

Back

It represents a system of equations with one unique solution.

Front

What does the graph of parallel lines indicate about a system of equations?

Back

It indicates that the system has no solution.

Front

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

Back

The lines are coincident, meaning they lie on top of each other.

Front

How do you determine the solution of a system of equations graphically?

Back

By finding the point where the lines intersect on the graph.

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

What does the slope of a line represent in a graph?

Back

The slope represents the rate of change of y with respect to x.

Front

How can you tell if two lines are parallel from their equations?

Back

If they have the same slope but different y-intercepts.

Front

What is the first step in graphing a system of equations?

Back

Convert each equation to slope-intercept form if necessary.