Systems of Equations 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 the other variable to be solved directly.

Front

What is the first step in the elimination method?

Back

The first step is to arrange the variables into columns.

Front

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

Back

You can eliminate a variable by adding or subtracting the equations in such a way that one of the variables cancels out.

Front

What is the solution to the system of equations X + 3Y = 23 and X - 3Y = 17?

Back

The solution is (20, 1).

Front

What is the solution to the system of equations X + Y = 6 and X - Y = 4?

Back

The solution is (5, 1).

Front

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

Back

A consistent system of equations has at least one solution.

Front

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

Back

An inconsistent system of equations has no solutions.

Front

What is a dependent system of equations?

Back

A dependent system of equations has infinitely many solutions, as the equations represent the same line.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations.

Front

What is the significance of the coefficients in a system of equations?

Back

The coefficients determine the slope and position of the lines represented by the equations.