Systems of Equations 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 for a system of equations to have one solution?

Back

The lines intersect at exactly one point.

Front

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

Back

The lines are parallel and never intersect.

Front

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

Back

The lines coincide, meaning they are the same line.

Front

How do you graph a linear equation?

Back

Identify the y-intercept and slope, then plot the points.

Front

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

Back

The slope is 'm', which indicates the steepness of the line.

Front

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

Back

The y-intercept is 'b', the point where the line crosses the y-axis.

Front

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

Back

By finding the point where the lines intersect.

Front

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

Back

(-1, -2)

Front

If two lines intersect at (3, 3), what does this point represent?

Back

It is the solution to the system of equations represented by the lines.