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

Back

It means the lines intersect at exactly one point.

Front

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

Back

It means the lines are parallel and never intersect.

Front

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

Back

It means the lines coincide, or are the same line.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point into each equation; if it satisfies both, it is a solution.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the graphs of the equations on the same coordinate plane.

Front

What is the solution to the system of equations y = 2x + 1 and y = -x + 4?

Back

(1, 3) - The lines intersect at this point.

Front

What is the significance of the slope in a system of equations?

Back

The slope indicates the steepness of the line; lines with the same slope are parallel.

Front

What is the y-intercept in the equation of a line?

Back

It is the point where the line crosses the y-axis.

Front

How can you tell if two lines are parallel from their equations?

Back

If they have the same slope but different y-intercepts.