Flashcard 6-1: System 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 for a system of equations to have one solution?

Back

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

Front

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

Back

The lines are parallel and never intersect.

Front

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

Back

The lines coincide, meaning they are the same line.

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

How can you determine if two lines are parallel?

Back

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

Front

What is the graphical representation of the equation y = x?

Back

A diagonal line that passes through the origin with a slope of 1.

Front

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

Back

By identifying the point where the lines intersect.

Front

What is the parent function of linear equations?

Back

y = x, which is the simplest form of a linear function.

Front

What does the term 'intersecting lines' refer to in a system of equations?

Back

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