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 elimination mean in the context of systems of equations?

Back

Elimination is a method used to solve systems of equations by removing one variable, allowing for the other variable to be solved.

Front

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

Back

You can eliminate a variable by adding or subtracting the equations in such a way that one variable cancels out.

Front

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

Back

The first step is to align the equations and make the coefficients of one variable the same or opposites.

Front

Solve using elimination: 7x + 2y = 24 and 8x + 2y = 30.

Back

(6, -9)

Front

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

Back

(7, -1)

Front

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

Back

(5, -8)

Front

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

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

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

Back

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

Front

Solve for x and y: 3x - 3y = 33 and 6x - 3y = 57.

Back

(8, -3)