Solving by Elimination - Addition

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 is the first step in using the elimination method?

Back

The first step is to align the equations so that the coefficients of one variable are opposites, allowing for easy elimination when the equations are added or subtracted.

Front

Given the equations 2x - y = -15 and -2x + 3y = 30, what is the result of adding them together?

Back

5y = 45.

Front

How do you solve the system of equations x + y = 6 and -x + y = 4 using elimination?

Back

Add the two equations to eliminate x: (x + y) + (-x + y) = 6 + 4, resulting in 2y = 10, so y = 5. Substitute y back to find x: x + 5 = 6, thus x = 1.

Front

What is the solution to the system of equations 4x + 8y = 20 and -4x + 2y = -30?

Back

The solution is (7, -1).

Front

What does it mean if two equations are dependent?

Back

Dependent equations have infinitely many solutions, as they represent the same line in a graph.

Front

What does it mean if two equations are inconsistent?

Back

Inconsistent equations have no solution, as they represent parallel lines that never intersect.

Front

Which of the following is NOT a method to solve systems of equations?

Back

Factoring.

Front

What is the solution to the system of equations -8x - 10y = 20 and -8x - 6y = -4?

Back

The solution is (5, -6).

Front

What is the purpose of the elimination method?

Back

The purpose is to simplify the process of solving systems of equations by eliminating one variable, making it easier to solve for the other.