Solving systems by elimination

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

Front

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

Back

You can choose to eliminate the variable that will simplify the calculations. Look for coefficients that are opposites or can be made opposites through multiplication.

Front

What do you multiply the equation 4x + 9y = 28 by to eliminate x when paired with -4x - y = -28?

Back

Multiply the first equation by -1.

Front

If you have the equations 2x + 3y = 6 and 4x + 6y = 12, what can you conclude about the system?

Back

The system has infinitely many solutions because the second equation is a multiple of the first.

Front

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

Back

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

Front

Solve by elimination: 3x + 4y = 10 and 6x + 8y = 20. What is the solution?

Back

The system has infinitely many solutions.

Front

What happens if the elimination method leads to a false statement, like 0 = 5?

Back

It indicates that the system of equations has no solution and is inconsistent.

Front

Solve by elimination: -x + 2y = 17 and 2x + 2y = -10. What is the solution?

Back

(-9, 4) is the solution.

Front

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

Back

Multiplying an equation allows you to create coefficients that can be added or subtracted to eliminate a variable.

Front

In the equations 4x + 8y = 20 and -4x + 2y = -30, which variable will be eliminated?

Back

The variable x will be eliminated.