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 using elimination?

Back

It means to eliminate one variable by adding or subtracting the equations, making it easier to solve for the remaining variable.

Front

What is the elimination method?

Back

A method for solving systems of equations by eliminating one variable, allowing for the other variable to be solved directly.

Front

What is the first step in the elimination method?

Back

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

Front

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

Back

You can multiply one or both equations by a number to make the coefficients of one variable equal, then add or subtract the equations.

Front

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

Back

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

Front

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

Back

(6, -9)

Front

Solve by elimination: 9x - 4y = 7 and x - 4y = -17.

Back

(3, 5)

Front

Solve by elimination: -6x + 5y = 1 and 6x + 4y = -10.

Back

(-1, -1)