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 a system of equations to have one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

The lines representing the equations are the same line, overlapping completely.

Front

How do you find the solution to a system of equations by graphing?

Back

Graph both equations on the same coordinate plane and identify the point of intersection.

Front

What is slope-intercept form of a linear equation?

Back

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

Front

How do you convert from standard form to slope-intercept form?

Back

Isolate y on one side of the equation.

Front

What is the slope of a line?

Back

The slope is the ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

What is the y-intercept of a line?

Back

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

Front

If two lines intersect at (4, -2), what does this point represent?

Back

This point is the solution to the system of equations represented by the two lines.