Elimination with Multiplication

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

How do you determine which equation to multiply in the elimination method?

Back

Choose the equation that, when multiplied, will allow the coefficients of one variable to be opposites, facilitating elimination.

Front

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

Back

Multiplying an equation adjusts the coefficients of the variables to align them for elimination, allowing for easier solving of the system.

Front

What does it mean to have a system of equations with no solution?

Back

A system of equations has no solution when the lines represented by the equations are parallel, meaning they never intersect.

Front

What does it mean to have a system of equations with infinitely many solutions?

Back

A system of equations has infinitely many solutions when the equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

Substitute the values of the variables back into the original equations to see if they satisfy both equations.

Front

What is the first step in using the elimination method?

Back

The first step is to align the equations and decide which variable to eliminate.

Front

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

Back

Coefficients determine how the equations interact; they must be manipulated to create opposites for effective elimination.

Front

What is a common mistake when using the elimination method?

Back

A common mistake is failing to multiply the equations correctly, leading to incorrect coefficients and an invalid solution.

Front

How do you handle fractions in the elimination method?

Back

To handle fractions, multiply the entire equation by the least common denominator to eliminate the fractions before proceeding.