Solving Systems of Equations by Elimination

Front

What is the elimination method for 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

How do you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines, meaning they have the same slope but different y-intercepts.

Front

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

Back

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

Front

What is the first step in using the elimination method?

Back

The first step is to align the equations and manipulate them (if necessary) so that the coefficients of one variable are opposites.

Front

How can you manipulate equations to prepare for elimination?

Back

You can multiply one or both equations by a constant to make the coefficients of one variable opposites.

Front

What is the solution to the system of equations 4x - 6y = -6 and -2x - 12y = -12?

Back

The solution is (0, 1).

Front

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

Back

It means to multiply one or both equations by a number to make the coefficients of one variable the same or opposites for elimination.

Front

What is the solution to the system of equations 3x + 7y = 23 and -3x - 7y = -17?

Back

The system has no solution.

Front

What is the solution to the system of equations 9x - 4y = 7 and x - 4y = -17?

Back

The solution is (3, 5).

Front

What is the solution to the system of equations 4x + 9y = 28 and -4x - y = -28?

Back

The solution is (7, 0).