Systems of Equations - elimination

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to solve a system of equations by elimination?

Back

It means to eliminate one variable by adding or subtracting the equations, allowing you to solve for the other variable.

Front

What is the elimination method?

Back

A technique used to solve systems of equations by eliminating one variable, making it easier to solve for the other.

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

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

Back

It means the equations represent the same line, and every point on that line is a solution.

Front

What is the first step in solving a system of equations by elimination?

Back

Align the equations and manipulate them to have the same coefficient for one of the variables.

Front

Solve the system: 5x + 16y = -16 and -9x - 8y = 8.

Back

(0, -1)

Front

Solve the system: 3x + 2y = 16 and 7x + y = 19.

Back

(2, 5)

Front

Solve the system: -8x - 10y = 20 and -8x - 6y = -4.

Back

(5, -6)

Front

Solve the system: 4x + 8y = 20 and -4x + 2y = -30.

Back

(7, -1)