4.8 Writing Systems

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables. Solutions are the points where the equations intersect.

Front

Define variables in the context of a system of equations.

Back

Symbols used to represent unknown values in equations, typically denoted as x, y, etc.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.

Front

What is a dependent system of equations?

Back

A system that has infinitely many solutions, where the equations represent the same line.

Front

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

Back

Identify variables, translate the relationships and conditions into equations.

Front

What is the graphical method of solving systems of equations?

Back

Plotting the equations on a graph to find the point(s) of intersection.