Systems: Choose the Method

Front

What is the elimination method in 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

When is the substitution method most useful?

Back

The substitution method is most useful when one equation can be easily solved for one variable in terms of the other.

Front

What is the graphing method for solving systems of equations?

Back

The graphing method involves plotting both equations on a graph to find the point(s) where they intersect, which represents the solution.

Front

What is a system of equations?

Back

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

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means there is no solution to the system, as the lines never intersect.

Front

What does it mean if two lines intersect at one point in a system of equations?

Back

If two lines intersect at one point, it means there is exactly one solution to the system.

Front

What does it mean if two lines coincide in a system of equations?

Back

If two lines coincide, it means there are infinitely many solutions, as they represent the same line.

Front

How do you decide which method to use for solving a system of equations?

Back

The choice of method depends on the specific equations; use substitution for easy isolation, elimination for straightforward addition/subtraction, and graphing for visual representation.

Front

What is the first step in the elimination method?

Back

The first step is to align the equations and manipulate them to have the same coefficient for one of the variables.

Front

What is the first step in the substitution method?

Back

The first step is to solve one of the equations for one variable in terms of the other.