Solving Systems of Equations: Graphing and Substitution

Front

What is the solution to a system of equations?

Back

Any ordered pair that makes both equations true.

Front

Why do parallel lines never intersect?

Back

Because they have the same slope.

Front

What does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never meet.

Front

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

Back

The lines representing the equations are the same line.

Front

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

Back

If they have the same slope.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the graphing method in solving systems of equations?

Back

A method where each equation is graphed on the same coordinate plane, and the point of intersection is the solution.

Front

What is an ordered pair?

Back

A pair of numbers (x, y) that represent a point on a coordinate plane.

Front

What does it mean for two lines to intersect?

Back

They meet at a single point, which is the solution to the system of equations.

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.