[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 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 there are countless sets of values for the variables that satisfy all equations, often because the equations represent the same line.

Front

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

Back

By graphing the equations and observing the intersection points: one intersection (unique), no intersection (no solution), or overlapping lines (infinitely many).

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of the line, calculated as the rise over run (change in y over change in x).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the point of intersection of two lines?

Back

The point where the two lines meet, representing the solution to the system of equations.

Front

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

Back

By plotting both equations on the same graph and identifying the point(s) where they intersect.