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 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, allowing for the other to be solved.

Front

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

Back

By adding or subtracting the equations to cancel out one of the variables.

Front

What does it mean if a system of equations has an infinite number of solutions?

Back

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

Front

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

Back

The equations represent parallel lines that never intersect.

Front

Solve using elimination: 3x + 2y = –13 and 3x + 4y = 1.

Back

(-9, 7)

Front

Solve using elimination: -4x + 9y = 9 and x - 3y = -6.

Back

(9, 5)

Front

Solve using elimination: -8x - 10y = 20 and -8x - 6y = -4.

Back

(5, -6)

Front

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

Back

(7, -1)