Mod 7 Rev. Systems of Equations and Inequalities (alg)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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 graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane, where the intersection points represent the solutions.

Front

What is an inequality?

Back

A mathematical statement that compares two expressions, indicating that one is greater than, less than, or not equal to the other.

Front

How do you represent a system of inequalities graphically?

Back

By shading the regions of the graph that satisfy each inequality, with the solution being the overlapping shaded area.

Front

What is the substitution method for 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 for solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

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

Back

A system that has at least one solution.

Front

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

Back

A system that has no solutions, meaning the lines are parallel.

Front

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

Back

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