Systems of Equations- graphing and substitution flashcard

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 infinite solutions?

Back

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

Front

How do you solve a system of equations by substitution?

Back

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

Front

What is the graphical representation of a system of equations?

Back

The solution is where the graphs of the equations intersect.

Front

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

Back

(6, 1)

Front

What does it indicate if two lines intersect at a single point?

Back

The system has a unique solution.

Front

What is the solution to the system: 2x + 3y = 6 and 4x + 6y = 12?

Back

Infinite solutions.

Front

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

Back

Graph each equation on the same coordinate plane.

Front

What does the point (1, 3) represent in a system of equations?

Back

It is a solution where both equations are satisfied.