Systems # of solutions

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 linear equations has one solution?

Back

The lines represented by the equations intersect at exactly one point.

Front

What are the possible types of solutions for a system of linear equations?

Back

One solution, no solution, or infinitely many solutions.

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

What is the graphical representation of a system with infinitely many solutions?

Back

The lines represented by the equations coincide, meaning they are the same line.

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

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

What does the term 'intersecting lines' refer to in the context of linear equations?

Back

Lines that cross each other at one point, indicating a unique solution.

Front

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

Back

It represents the solution to the system, where the values satisfy all equations.

Front

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

Back

By analyzing the positions of the lines: intersecting, parallel, or coinciding.