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 eliminate a variable in a system of equations?

Back

To remove one variable by combining 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 adding or subtracting equations to eliminate a variable.

Front

What is a solution set in the context of systems of equations?

Back

The set of all possible solutions that satisfy all equations in the system.

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 infinitely many solutions?

Back

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

Front

How do you determine if two equations are equivalent?

Back

If one equation can be transformed into the other by algebraic manipulation.

Front

What is the first step in solving the equation 5 - 2(x - 7) = x + 1 + 3x?

Back

Distributing -2 to (x - 7).

Front

What is the first step in solving the equation 5x + 7 = 12?

Back

Subtract 7 from both sides.

Front

What is the solution to the equation 3(x - 1) = 2x + 9?

Back

x = 12.