System of Equations; Number of solutions and solving by graphing

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 graphs of the equations intersect at exactly one point.

Front

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

Back

The graphs of the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The graphs of the equations are the same line.

Front

How can you determine the number of solutions in a system of equations by graphing?

Back

By observing the intersection points of the lines.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane.

Front

What is the slope of a line in the equation y = mx + b?

Back

The slope (m) represents the steepness and direction of the line.

Front

What does the y-intercept represent in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis.

Front

If two lines are parallel, what can be said about their slopes?

Back

They have the same slope but different y-intercepts.

Front

What is the solution to the system of equations: y = 2x + 1 and y = 2x - 3?

Back

No Solution (the lines are parallel).