Elimination - Without Common Coefficients

Front

What is the elimination method in solving systems of equations?

Back

The elimination method is a technique used to solve systems of linear equations by eliminating one variable, allowing for the other variable to be solved directly.

Front

What does it mean to have 'no common coefficients' in elimination?

Back

'No common coefficients' means that the coefficients of the variables in the equations do not share a common factor, which may require manipulation of the equations to align coefficients for elimination.

Front

How do you manipulate equations to use the elimination method?

Back

You can multiply one or both equations by a constant to create equal or opposite coefficients for one of the variables, allowing for elimination.

Front

What is the first step in solving the system of equations 9x + 3y = 12 and 2x + y = 5 using elimination?

Back

The first step is to manipulate the equations to align the coefficients of either x or y for elimination.

Front

What is the solution to the system of equations 9x + 3y = 12 and 2x + y = 5?

Back

The solution is (-1, 7).

Front

What is the solution to the system of equations 3x + 3y = 9 and 5x + 4y = 10?

Back

The solution is (-2, 5).

Front

How do you check the solution of a system of equations?

Back

Substitute the values of the solution into both original equations to verify that both equations hold true.

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.