Systems of Equations

Front

What is a system of equations?

Back

A set of two or more 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

How do you convert an equation to slope-intercept form?

Back

Rearrange the equation to the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of the line represented by the equation y = -2x + 7?

Back

The slope is -2.

Front

What is the y-intercept of the line represented by the equation y = 5x + 3?

Back

The y-intercept is 3.

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 a system with one solution?

Back

Two lines that intersect at a single point.

Front

What is the graphical representation of a system with no solution?

Back

Two parallel lines that never meet.