Systems of Equations Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does substitution mean in the context of systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable. 4. Substitute back to find the first variable.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate system, typically written as (x, y).

Front

What does it mean if two equations are consistent?

Back

Two equations are consistent if they have at least one solution.

Front

What does it mean if two equations are inconsistent?

Back

Two equations are inconsistent if they have no solutions.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations.

Front

What is the significance of the intersection point in a system of equations?

Back

The intersection point represents the solution to the system, where both equations are satisfied.

Front

What is a dependent system of equations?

Back

A dependent system has infinitely many solutions, meaning the equations represent the same line.

Front

What is an independent system of equations?

Back

An independent system has exactly one solution, meaning the lines intersect at one point.