Elimination method

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 does it mean if a system of equations has an infinite number of solutions?

Back

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

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

How do you determine the solution to a system of equations graphically?

Back

The solution is the point where the two lines intersect on the graph.

Front

What is the first step in using the elimination method?

Back

The first step is to align the equations so that corresponding variables and constants are in the same columns.

Front

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

Back

You can eliminate a variable by adding or subtracting the equations after multiplying them by suitable coefficients.

Front

Solve the system using elimination: 2x + 3y = 6 and 4x + 6y = 12.

Back

Infinite number of solutions.

Front

Solve the system using elimination: 3x + 2y = 12 and 3x - 4y = 0.

Back

(4, 0).

Front

What is the solution to the system: x + y = 5 and x - y = 1?

Back

(3, 2).

Front

What is the significance of the coefficients in the elimination method?

Back

The coefficients determine how the equations can be manipulated to eliminate a variable.