[2] u5d8 Mix Review

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

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

Back

It means that there are no values for the variables that can satisfy all equations in the system, often because the lines are parallel.

Front

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

Back

It means that there are an infinite number of values for the variables that satisfy all equations, often because the equations represent the same line.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

How can you determine if two lines are the same?

Back

Two lines are the same if they have the same slope and the same y-intercept.

Front

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

Back

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

Front

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

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

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

Back

The point of intersection represents the solution to the system, where the values of the variables satisfy all equations.

Front

If a system of equations has a unique solution, what does the graph look like?

Back

The graph will show two lines that intersect at exactly one point.