Graphing Systems of Equations

Front

What is a system of equations?

Back

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

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point, which is the solution.

Front

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

Back

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

Front

How do you determine if an ordered pair is a solution to a system of equations?

Back

Substitute the ordered pair into both equations; if it satisfies both, it is a solution.

Front

What is the graphical representation of the equation y = mx + b?

Back

A straight line where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope (m) is the ratio of the rise (change in y) to the run (change in x).

Front

How do you find the intersection point of two lines graphically?

Back

Graph both lines on the same coordinate plane and identify the point where they cross.

Front

What is the y-intercept of an equation?

Back

The y-intercept is the point where the line crosses the y-axis (x=0).

Front

What is the x-intercept of an equation?

Back

The x-intercept is the point where the line crosses the x-axis (y=0).