Solving Systems of Equations by 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 two lines to intersect?

Back

It means they have a common solution, which is the point where they meet.

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect.

Front

What does it mean if two lines are parallel?

Back

They have no solutions because they never intersect.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the graphs of the equations: one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (same line).

Front

What is the slope of a line?

Back

The rate at which the line rises or falls, calculated as the change in y over the change in x.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How do you graph a linear equation?

Back

By plotting points that satisfy the equation and connecting them to form a line.

Front

What is the significance of the point of intersection in a graph?

Back

It represents the solution to the system of equations.