Systems of Equations Graphically

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 one solution?

Back

The graphs of the equations intersect at exactly one point.

Front

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

Back

The graphs of the equations are parallel and never intersect.

Front

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

Back

The graphs of the equations coincide, meaning they are the same line.

Front

How can you determine the solution of a system of equations graphically?

Back

By finding the point(s) where the graphs of the equations intersect.

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.

Front

What is the slope of a line?

Back

The rate at which y changes for a change in x, often represented as 'm' in the equation y = mx + b.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis, represented as 'b' in the equation y = mx + b.

Front

How do you find the intersection point of two lines graphically?

Back

By plotting both lines on the same graph and identifying the point where they cross.

Front

What is the significance of the solution (6, 3) in a system of equations?

Back

It represents the point where the two equations intersect, indicating the values of x and y that satisfy both equations.