Systems of Linear Equations (Warm-Up)

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean if a system has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system has one solution?

Back

The lines intersect at exactly one point.

Front

What does it mean if a system has infinitely many solutions?

Back

The lines are the same, meaning they overlap completely.

Front

How can you determine the number of solutions in a system of equations?

Back

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

Front

What is the slope of a line?

Back

The steepness of the line, calculated as the rise over run.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

What is an ordered pair?

Back

A pair of numbers (x, y) that represent a point on a coordinate plane.

Front

How do you check if an ordered pair is a solution to a system?

Back

Substitute the x and y values into both equations to see if they hold true.

Front

What does the notation f(x) represent?

Back

It represents a function named 'f' evaluated at the input 'x'.