Systems 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 does the solution of a system represent?

Back

The solution of a system represents the ordered pair that satisfies all equations in the system.

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

What is the graphical representation of intersecting lines?

Back

Intersecting lines represent a system of equations with one unique solution.

Front

What is the elimination method?

Back

The elimination method is a technique used to solve systems of equations by eliminating one variable.

Front

If a system of equations has infinitely many solutions, what does the graph look like?

Back

The graph consists of overlapping lines, indicating that the equations are equivalent.

Front

What is the ordered pair solution for the equations y = 2x + 1 and y = 3x - 2?

Back

The solution is (1, 3).

Front

How can you determine if a system of equations has a unique solution?

Back

If the lines represented by the equations intersect at one point, the system has a unique solution.

Front

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

Back

Solve one of the equations for one variable in terms of the other.

Front

What does it mean for two lines to be skew?

Back

Skew lines are lines that do not intersect and are not parallel, existing in different planes.