ELIMINATION Learning Check (systems of equations)

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 do you need to multiply the top equation by to create a zero pair?

Back

You need to multiply the top equation by a value that will make the coefficients of one of the variables equal and opposite in the two equations.

Front

If you multiply the equation 2x + 3y = 12 by -2, what is the new equation?

Back

-4x - 6y = -24.

Front

In the elimination method, which variable do you typically aim to eliminate first?

Back

You typically aim to eliminate either the x or y variable, depending on which is easier based on the coefficients.

Front

What does it mean to create a zero pair in elimination?

Back

Creating a zero pair means adjusting the equations so that when added together, one variable cancels out to equal zero.

Front

How do you determine which variable to eliminate in a system of equations?

Back

You look for the variable with coefficients that can easily be manipulated to create a zero pair.

Front

What is the first step in solving a system of equations using elimination?

Back

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

Front

What is the solution to the system of equations 7x - 9y = 29 and 7x + 2y = -15?

Back

The solution is (-1, -4).

Front

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

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means that the equations represent the same line, and every point on that line is a solution.