INTRO Systems of Linear Equations

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 of equations has one solution?

Back

The lines intersect at exactly one point, representing a unique solution.

Front

What does it mean if a system of equations has no solution?

Back

The lines are parallel and never intersect.

Front

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

Back

The lines coincide, meaning they are the same line.

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 solution to a system of equations?

Back

The point(s) where the equations intersect on a graph.

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x).

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

How do you graph a linear equation?

Back

By plotting points that satisfy the equation and connecting them.

Front

What is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are constants.