Solving Systems by Graphing & Substitution

Front

What does the graph of a system of equations with no solution look like?

Back

The graph consists of parallel lines.

Front

What is the solution to a system of equations?

Back

The point that the equations have in common.

Front

If two lines intersect at a point, what does that point represent?

Back

The solution to the system of equations.

Front

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

Back

The lines coincide, meaning they are the same line.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect.

Front

What is the solution to the system of equations: x = -3y - 8 and x - 2y = -3?

Back

(-5, -1) is the solution.

Front

What does it mean if two lines are skew?

Back

They do not intersect and are not parallel, existing in different planes.

Front

What is the graphical representation of a system with exactly one solution?

Back

Two lines that intersect at a single point.

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable.