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 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 a system of equations?

Back

No common coefficients means that the coefficients of the variables in the equations do not match, making it impossible to eliminate a variable directly without manipulation.

Front

How can we create common coefficients in a system of equations?

Back

We can create common coefficients by multiplying one or both equations by a suitable number so that the coefficients of one variable become the same.

Front

What is the first step in using the elimination method?

Back

The first step is to arrange the equations in standard form (Ax + By = C) if they are not already.

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 value of Y when solving the problem: 9x + 3y = 12 and 2x + y = 5?

Back

Y = 7.

Front

What is the value of X when solving the problem: 3x + 3y = 9 and 5x + 4y = 10?

Back

X = -2.

Front

What is the value of X when solving the problem: x + 3y = 6 and 2x - 7y = -1?

Back

X = 3.

Front

What should you do if you cannot eliminate a variable directly?

Back

You should multiply one or both equations by a number to create common coefficients.

Front

What is the significance of the elimination method in algebra?

Back

The elimination method allows for the systematic solving of systems of equations, making it easier to find the values of variables.