Solving Systems of Equations By Elimination

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

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

Back

A system of equations has no solution if the equations represent parallel lines that never intersect.

Front

How do you determine if a variable can be eliminated in a system of equations?

Back

A variable can be eliminated if the coefficients of that variable in both equations are opposites or can be made opposites through multiplication.

Front

What is the first step in using the elimination method?

Back

The first step is to align the equations so that like terms are in the same column, making it easier to add or subtract them.

Front

What is the resulting equation when you add the equations 4x + 4y = 4 and 3x + 4y = 10?

Back

The resulting equation is 7x + 8y = 14.

Front

What does the term 'combined equation' refer to in the context of elimination?

Back

The combined equation is the result of adding or subtracting the original equations to eliminate one variable.

Front

What is the significance of the coefficients in the elimination method?

Back

The coefficients determine how the equations can be manipulated to eliminate a variable; they must be compatible for elimination to occur.

Front

How can you check if your solution to a system of equations is correct?

Back

You can check the solution by substituting the values back into the original equations to see if they hold true.

Front

What is the result of adding the equations -2x + 6y = -20 and 2x + 5y = -13?

Back

The result is 11y = -33.

Front

What does it mean for two equations to be dependent?

Back

Two equations are dependent if they represent the same line, resulting in infinitely many solutions.