Solving Systems by Elimination

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean to solve a system of equations by elimination?

Back

It means to eliminate one variable by adding or subtracting the equations, allowing you to solve for the other variable.

Front

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

Back

Align the equations so that like terms are in the same column.

Front

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

Back

You can multiply one or both equations by a number to make the coefficients of one variable opposites, then add or subtract the equations.

Front

What is the solution to a system of equations?

Back

The point (x, y) where the two lines intersect, representing the values of the variables that satisfy both equations.

Front

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

Back

It means the lines are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

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

Front

What is the elimination method used for?

Back

To find the values of variables in a system of equations by eliminating one variable.

Front

What is the result of adding the equations 4x - 6y = 20 and 4x + 6y = -4?

Back

The result is 8x = 16, which simplifies to x = 2.

Front

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

Back

Coefficients determine the slope and position of the lines represented by the equations.