Systems of Equations Elimination

Front

What is a system of equations?

Back

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

Front

What does it mean for two lines to be parallel in a system of equations?

Back

Parallel lines have no points in common, meaning they have no solutions.

Front

What is the elimination method in solving systems of equations?

Back

A method where you add or subtract equations to eliminate one variable.

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

One solution: lines intersect at one point; no solution: lines are parallel; infinitely many solutions: lines are the same.

Front

What is the first step in using the elimination method?

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

Solve using elimination: 4x + 8y = 20 and -4x + 2y = -30.

Back

(7, -1)

Front

Solve using elimination: 2x + 3y = 12 and 5x - y = 13.

Back

(3, 2)

Front

What does it mean to multiply an equation in a system?

Back

To make the coefficients of one variable the same in both equations for elimination.

Front

Solve using elimination: -x + y = -13 and -8x - 4y = -8.

Back

(5, -8)

Front

What is a consistent system of equations?

Back

A system that has at least one solution.