Solving System 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 two equations to be equivalent?

Back

They represent the same line when graphed, meaning they have the same solution.

Front

What is the graphical method for solving a system of equations?

Back

Plotting both equations on the same graph and identifying their point of intersection.

Front

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

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines coincide when graphing a system of equations?

Back

The system has infinite solutions because every point on the line is a solution.

Front

What is the constant of variation in a direct variation equation?

Back

It is the non-zero constant 'k' in the equation y = kx.

Front

How do you find the constant of variation from a direct variation problem?

Back

Divide y by x (k = y/x).

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

How can you determine if a relationship is a direct variation?

Back

If the equation can be written in the form y = kx, where k is a constant.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where both equations are satisfied.