Flashcard 6: 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 a unique solution?

Back

It means that the equations intersect at exactly one point on the graph.

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

It means that the equations represent the same line, so every point on the line is a solution.

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

Back

By plotting both equations on the same graph and identifying the point of intersection.

Front

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

Back

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

Front

What is the significance of the coefficients in a linear equation?

Back

They determine the slope and position of the line on the graph.

Front

What is the parent function of linear equations?

Back

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

Front

How can you determine if two lines are parallel?

Back

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