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 two lines are parallel in a system of equations?

Back

They have no solutions because they never intersect.

Front

What does it mean if two lines are the same in a system of equations?

Back

They have an infinite number of solutions because they overlap completely.

Front

What does it mean if two lines intersect in a system of equations?

Back

They have one unique solution, which is the point of intersection.

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 graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane.

Front

What is the solution to the system of equations y = 2x + 1 and y = 2x - 3?

Back

No Solution (the lines are parallel).

Front

What is the solution to the system of equations y = -x + 4 and y = x - 2?

Back

(3, 1) (the lines intersect at this point).

Front

What does the term 'consistent' mean in relation to a system of equations?

Back

A consistent system has at least one solution.

Front

What does the term 'inconsistent' mean in relation to a system of equations?

Back

An inconsistent system has no solutions.