Systems of Equations- Algebra 2 - Solving by graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system of equations to have one solution?

Back

It means 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

It means 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

It means the equations represent the same line, so they intersect at every point on that line.

Front

How can you determine the solution of a system of equations by graphing?

Back

By plotting the equations on the same set of axes and identifying the point(s) where they intersect.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of the line, calculated as the rise over run.

Front

What is the y-intercept of a line?

Back

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

Front

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

Back

By locating the point where the two lines cross on the graph.

Front

What is the significance of the point (0,0) in a system of equations?

Back

It is the origin and can be a solution if both equations pass through this point.