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 eliminating one variable, allowing for the other variable to be solved directly.

Front

How do you eliminate a variable in a system of equations?

Back

To eliminate a variable, you can add or subtract the equations in such a way that one of the variables cancels out.

Front

What is the first step in using the elimination method?

Back

The first step is to align the equations and, if necessary, multiply one or both equations by a constant to make the coefficients of one variable the same.

Front

Solve by elimination: 4x + 4y = 4 and 3x + 4y = 10.

Back

(-6, 7)

Front

Solve by elimination: 4x + 9y = 28 and -4x - y = -28.

Back

(7, 0)

Front

Solve by elimination: 9x - 4y = 7 and x - 4y = -17.

Back

(3, 5)

Front

Solve by elimination: -9x - 4y = -20 and 5x + 4y = 4.

Back

(4, -4)

Front

Solve by elimination: x + 9y = 8 and -6x - 9y = -3.

Back

(-1, 1)

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.