Systems of Equations Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

Where do we start graphing a line if there is no constant term?

Back

At the origin (0,0).

Front

What does it mean for two lines to intersect on a graph?

Back

It means that the solution to the system of equations is the point where the two lines meet.

Front

What is the solution to a system of equations?

Back

The point (x, y) where the equations intersect.

Front

If two lines are parallel, what can we say about their solutions?

Back

There is no solution, as parallel lines never intersect.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of the line, calculated as the rise over run.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis.

Front

How can you determine the y-intercept from the equation of a line?

Back

It is the constant term when the equation is in the form y = mx + b.

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.