Systems

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 equations represent parallel lines that never intersect.

Front

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

Back

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

Front

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

Back

By analyzing the slopes and intercepts of the lines represented by the equations.

Front

What is the graphical representation of intersecting lines?

Back

It indicates that there is exactly one solution to the system.

Front

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

Back

(1, 5) is the solution.

Front

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

Back

Infinitely many solutions, as the second equation is a multiple of the first.

Front

What does the term 'consistent' mean in relation to a system of equations?

Back

A consistent system has at least one solution.

Front

What does the term 'inconsistent' mean in relation to a system of equations?

Back

An inconsistent system has no solutions.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then substituted into the other equation.