Systems of equations graphing

Front

What are systems of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for two lines to be parallel?

Back

They have the same slope and will never intersect.

Front

What is the solution to a system of equations?

Back

The point where the equations intersect on a graph.

Front

What does it mean if a system of equations has no solution?

Back

The lines are parallel and do not intersect.

Front

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

Back

The lines are the same, meaning they overlap completely.

Front

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

Back

If their slopes (coefficients of x) are equal.

Front

What is the slope-intercept form of a line?

Back

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

Front

How do you find the slope of a line given two points?

Back

Use the formula (y2 - y1) / (x2 - x1).

Front

What does it mean for two lines to intersect?

Back

They cross at a single point, which is the solution to the system.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane.