Systems of linear equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations in the same variables.

Front

What does it mean if a system of linear equations has no solutions?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

Solve the system using elimination: 2x + 3y = 6 and 4x + 6y = 12.

Back

Infinite number of solutions.

Front

Solve the system using elimination: x + y = 5 and x - y = 1.

Back

(3, 2).

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 substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

If two equations represent the same line, what can we say about their solutions?

Back

They have infinitely many solutions.

Front

What is the graphical representation of a system of linear equations?

Back

The intersection points of the lines represent the solutions to the system.

Front

Solve the system using elimination: 3x + 2y = 12 and 6x + 4y = 24.

Back

Infinite number of solutions.