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 a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point, which is the solution to the system.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The lines representing the equations are the same line, meaning they overlap completely.

Front

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

Back

By finding the point where the lines intersect on a graph.

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 ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

How do you find the solution to a system of equations algebraically?

Back

By using methods such as substitution, elimination, or graphing.

Front

What is the substitution method?

Back

A method for solving a system of equations by solving one equation for one variable and substituting that value into the other equation.