Solving Systems by Graphing

Front

What is a system of equations?

Back

A set of two (or more) equations that share variables.

Front

What type of lines result in one solution when graphing a system of equations?

Back

Intersecting lines.

Front

What does it mean if two lines are parallel in a system of equations?

Back

They have no points in common, resulting in no solution.

Front

What does it mean if two lines are coinciding?

Back

They lie on top of one another, resulting in infinitely many solutions.

Front

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

Back

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

Front

What is the graphical representation of the equation y = 2x + 3?

Back

A straight line with a slope of 2 and a y-intercept of 3.

Front

What is the slope of the line represented by the equation y = -3x + 4?

Back

-3.

Front

If a system of equations has no solution, what can be said about the lines?

Back

The lines are parallel.

Front

What is the y-intercept of the equation y = 5x - 1?

Back

-1.

Front

How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

By analyzing the slopes and y-intercepts of the lines.