Systems of Equations 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 is the graphical representation of a system with infinitely many solutions?

Back

The lines representing the equations are the same line, overlapping each other.

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 solution of the system: 2x + 3y = 6 and x - y = 1?

Back

(3,0)

Front

What does it mean if two lines intersect at a point?

Back

The system of equations has one unique solution.

Front

What is the substitution method?

Back

A method for solving systems of equations by replacing one variable with an expression from another equation.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate a variable.

Front

What is the solution of the system: 3x + 4y = 12 and 6x + 8y = 24?

Back

No solution (the second equation is a multiple of the first).

Front

What does it mean if a system of equations is consistent?

Back

The system has at least one solution.