System of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations that have the same variables.

Front

What are the possible types of solutions for a system of equations?

Back

One Solution, No Solution, Infinitely Many Solutions.

Front

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

Back

It means the lines intersect at one point.

Front

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

Back

It means the lines are parallel and never touch.

Front

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

Back

It means the lines are the same.

Front

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

Back

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

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, which is then substituted into the other equation.

Front

What does the graph of a system of equations with one solution look like?

Back

The graph shows two lines that intersect at a single point.

Front

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

Back

The graph shows two parallel lines that never intersect.