Systems, Picking Best 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 preferred over elimination?

Back

The substitution method is preferred when one equation is easily solvable for one variable, allowing for straightforward substitution into the other equation.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved simultaneously.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

Front

What is the graphical method of solving systems of equations?

Back

The graphical method involves plotting the equations on a graph and identifying the point(s) where they intersect.

Front

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

Back

Consider the form of the equations: use substitution if one equation is easily solvable for a variable; use elimination if the coefficients are conducive to cancellation.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

What is a dependent system of equations?

Back

A dependent system has infinitely many solutions, meaning the equations represent the same line.

Front

What is an independent system of equations?

Back

An independent system has exactly one solution, meaning the equations represent two intersecting lines.