Solving Systems by Elimination

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves manipulating equations to eliminate one variable, allowing for the solution of the remaining variable.

Front

What does it mean to align like terms in an equation?

Back

Aligning like terms means arranging terms with the same variable or constant together, typically in a vertical format for clarity.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into both equations. If both equations are satisfied, the point is a solution.

Front

What is the first step in using the elimination method?

Back

The first step is to manipulate the equations so that one variable can be eliminated when the equations are added or subtracted.

Front

What is the solution to the system of equations: 2x + 3y = 6 and 4x + 6y = 12?

Back

There are infinitely many solutions; the equations are dependent.

Front

What do you do if the coefficients of one variable are the same in both equations?

Back

You can subtract one equation from the other to eliminate that variable.

Front

What is the purpose of multiplying an equation in the elimination method?

Back

Multiplying an equation allows you to create equivalent equations that can be manipulated to eliminate a variable.

Front

Solve by elimination: 3x + 2y = 12 and 6x + 4y = 24.

Back

There are infinitely many solutions; the equations are dependent.

Front

What is the solution to the system of equations: x + y = 10 and x - y = 2?

Back

(6, 4) is the solution.

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.