System of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

It means the lines representing the equations are parallel and never intersect.

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How can you determine the number of solutions in a system of equations graphically?

Back

By analyzing the intersection points of the lines on a graph.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

What is the graphical representation of a system of equations?

Back

It is represented by lines on a coordinate plane.

Front

What is the significance of the point (0, 0) in a system of equations?

Back

It is the origin and can be a solution if it satisfies all equations in the system.

Front

How do you solve a system of equations using substitution?

Back

By solving one equation for one variable and substituting that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

By adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.