Solving Systems with Elimination

Front

What is a system of equations?

Back

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

Front

What does it mean for two lines to be parallel in a system of equations?

Back

It means they have no points in common and therefore no solutions.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves 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

By analyzing the slopes and intercepts of the lines represented by the equations.

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect.

Front

If two lines intersect at a point, how many solutions does the system have?

Back

One solution.

Front

What is the first step in using the elimination method?

Back

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

Front

How can you make the coefficients of one variable the same in both equations?

Back

By multiplying one or both equations by a suitable number.

Front

What does it mean if a system of equations is inconsistent?

Back

It means there are no solutions to the system.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.