Solving Systems by 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 by elimination?

Back

It means to eliminate one variable by adding or subtracting the equations to find the value of the other 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.

Front

What is the first step in the elimination method?

Back

Align the equations so that the coefficients of one variable are opposites.

Front

If you have the equations 2x + 3y = 6 and 4x + 6y = 12, what can you conclude?

Back

The equations are dependent; they represent the same line.

Front

What is the solution to the system of equations 3x + 2y = 12 and 3x - 2y = 6?

Back

(2, 3) is the solution.

Front

How do you eliminate the variable x in the equations 2x + 3y = 6 and 4x + 6y = 12?

Back

Multiply the first equation by -2 and add it to the second equation.

Front

What is the significance of the solution to a system of equations?

Back

It represents the point where the graphs of the equations intersect.

Front

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

Back

The lines are parallel and do not intersect.

Front

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

Back

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