Intro to Solving Systems of Equations (some Substitution)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

How can you tell if a point is a solution to a system of equations?

Back

The (x,y) coordinates make BOTH equations true.

Front

What does it mean for two equations to intersect on a graph?

Back

It means they have a common solution (x, y) that satisfies both equations.

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

When using substitution, what do you do first?

Back

Choose one equation and solve for one variable in terms of the other.

Front

What happens when you graph the same equation twice?

Back

You will have infinite solutions.

Front

What is the solution to a system of equations?

Back

The point (x, y) where the equations intersect.

Front

If a system of equations has no solution, what does that mean graphically?

Back

The lines are parallel and never intersect.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.