Systems: Elimination & Substitution

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

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What does it mean for a system of equations to have no solutions?

Back

A system has no solutions when the lines represented by the equations are parallel and have different y-intercepts.

Front

What does it mean for a system of equations to have infinite solutions?

Back

A system has infinite solutions when the lines represented by the equations are identical, meaning they overlap completely.

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

When is the elimination method preferred over substitution?

Back

The elimination method is preferred when the coefficients of one variable are easily manipulated to eliminate that variable.

Front

When is the substitution method preferred over elimination?

Back

The substitution method is preferred when one equation is already solved for one variable or can be easily rearranged.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the point(s) where the lines intersect, which represent the solution(s) to the system.

Front

How can you tell if two lines are parallel from their equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

How can you tell if two lines are identical from their equations?

Back

Two lines are identical if they have the same slope and the same y-intercept.