Systems of Linear Equations

Front

What is a system of linear equations?

Back

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

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What does it mean if two lines intersect at one point when graphing a system of linear equations?

Back

The system has one unique solution.

Front

What does it mean if two lines are parallel when graphing a system of linear equations?

Back

The system has no solution.

Front

What does it mean if two lines overlap when graphing a system of linear equations?

Back

The system has infinite solutions.

Front

What is the elimination method in solving systems of linear equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

Front

Solve by elimination: 2x + 3y = 6 and 4x + 6y = 12. What is the solution?

Back

Infinite solutions.

Front

Solve by elimination: x + y = 5 and x - y = 1. What is the solution?

Back

(3, 2).

Front

What is the substitution method in solving systems of linear equations?

Back

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

Front

Solve by substitution: y = 2x + 1 and 3x - y = 4. What is the solution?

Back

(1, 3).

Front

What is a consistent system of equations?

Back

A system that has at least one solution.