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 for a system of equations to have a solution?

Back

It means there is at least one ordered pair (x, y) that satisfies all equations in the system.

Front

What is the solution to the system of equations: y = 2x + 1 and y = 4x - 1?

Back

(1, 3)

Front

What do parallel lines represent in a system of equations?

Back

They represent a system of equations with no solution.

Front

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

Back

Two intersecting lines.

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)

Front

What is an ordered pair?

Back

A pair of numbers (x, y) that represent a point on a coordinate plane.

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 of equations with infinitely many solutions?

Back

Two overlapping lines.

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.