FM 3.5 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 has no solution if the equations represent parallel lines that never intersect.

Front

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

Back

A system has infinite solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

What is the first step in the elimination method?

Back

The first step is to manipulate the equations (by multiplying or adding) to align coefficients of one variable for elimination.

Front

How do you determine which variable to eliminate?

Back

Choose the variable that can be easily eliminated by aligning coefficients through multiplication or addition.

Front

What is the result of multiplying an equation by a non-zero constant?

Back

Multiplying an equation by a non-zero constant produces an equivalent equation, meaning it has the same solutions.

Front

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

Back

Aligning coefficients allows for the direct elimination of a variable when the equations are added or subtracted.

Front

If two equations are identical, what can be said about their solutions?

Back

If two equations are identical, they have infinite solutions as they represent the same line.

Front

What is the purpose of multiplying both equations by different numbers in the elimination method?

Back

Multiplying both equations by different numbers can help align coefficients for easier elimination of a variable.

Front

What does it mean if after elimination, you get a false statement like 0 = 5?

Back

A false statement indicates that the system has no solution, meaning the lines are parallel.