Systems of Equations Flashcard: Graphing and Substitution

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 a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

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

Back

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

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable, then substitute that expression into the other equation.

Front

What is the first step in solving the system by substitution?

Back

Isolate one variable in one of the equations.

Front

What is the solution to the system: y = 2x - 11 and 2x - 8y = 4?

Back

(6, 1)

Front

What does the equation 4 = 7 indicate when solving a system of equations?

Back

It indicates that there is no solution, as this statement is false.

Front

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

Back

Two lines that intersect at a single point.

Front

What is the graphical representation of a system with no solutions?

Back

Two parallel lines that never intersect.