Systems of Equations by 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 to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the elimination method?

Back

A technique for solving systems of equations by eliminating one variable to solve for the other.

Front

How do you eliminate a variable in a system of equations?

Back

By adding or subtracting the equations to cancel out one variable.

Front

What is a unique solution in a system of equations?

Back

A single set of values for the variables that satisfies all equations.

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 infinite solutions?

Back

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

Front

Solve using elimination: x - y = 11 and 2x + y = 19.

Back

(10, -1)

Front

Solve using elimination: x + 6y = 17 and -x + 3y = -8.

Back

(11, 1)

Front

Solve using elimination: 4x + 9y = 28 and -4x - y = -28.

Back

(7, 0)