12/10 bell-ringer

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations in the system.

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

Front

What does 'elimination' mean in solving systems of equations?

Back

Elimination is a method used to solve systems of equations by removing one variable, allowing for the solution of the remaining variable.

Front

What is the purpose of using variables in equations?

Back

Variables represent unknown values in equations, allowing us to formulate relationships and solve for those unknowns.

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution values back into the original equations to see if they satisfy all equations.

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients represent the rate of change of the dependent variable with respect to the independent variable in a linear equation.

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 is an ordered triple in the context of systems of equations?

Back

An ordered triple is a solution to a system of three equations with three variables, represented as (x, y, z).

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines (in two dimensions) or planes (in three dimensions) that show the relationships between the equations.

Front

What is the difference between dependent and independent equations?

Back

Dependent equations have infinitely many solutions (they represent the same line), while independent equations have exactly one solution (they intersect at one point).