Graphing 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 if two lines are parallel in a system of equations?

Back

They have no solutions because they never intersect.

Front

What does it mean if two lines intersect at one point?

Back

The system has one unique solution.

Front

What does it mean if two lines are identical?

Back

The system has infinitely many solutions.

Front

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

Back

By finding the point(s) where the lines intersect on the graph.

Front

What is the graphical representation of the equation y = mx + b?

Back

A straight line with slope m and y-intercept b.

Front

What is the slope of a line?

Back

The rate at which y changes for a change in x, often represented as 'm'.

Front

What does the y-intercept represent in a linear equation?

Back

The point where the line crosses the y-axis.

Front

How do you solve a system of equations by graphing?

Back

Graph each equation on the same set of axes and identify the intersection point.

Front

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

Back

No solution, as the lines are parallel.