Solving Systems of Equations by Elimination

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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 elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

If the lines intersect at one point, there is one solution. If the lines are parallel, there is no solution. If the lines coincide, there are infinitely many solutions.

Front

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

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

Given the equations 3x + 2y = 6 and 3x - 4y = 12, what is the first step to eliminate x?

Back

Multiply the first equation by -1 to make the coefficients of x opposites.

Front

What is the solution to the system of equations 2x + 3y = 6 and 4x + 6y = 12?

Back

The system has infinitely many solutions because the second equation is a multiple of the first.

Front

If you have the equations x + 2y = 8 and 3x + 2y = 14, how can you eliminate y?

Back

Subtract the first equation from the second to eliminate y.

Front

What is the result of eliminating y in the equations 5x - 2y = 10 and 3x + 2y = 6?

Back

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

Front

How do you check the solution of a system of equations?

Back

Substitute the values of the variables back into the original equations to see if they hold true.