How Many Solutions to a System?

Front

What is a system of equations?

Back

A set of two or more 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.

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 do you find the y-intercept of a linear equation?

Back

Set x = 0 and solve for y.

Front

What is the y-intercept of the equation y = -2x?

Back

0, because when x = 0, y = 0.

Front

What is the slope of the line represented by the equation y = mx + b?

Back

The slope is represented by 'm' in the equation.

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 intersecting at a single point.

Front

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

Back

Two parallel lines that never meet.