Systems Review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system to have a unique solution?

Back

A unique solution occurs when the graphs of the equations intersect at exactly one point.

Front

What is an infinite number of solutions in a system?

Back

This occurs when the equations represent the same line, meaning every point on the line is a solution.

Front

What does it mean if a system has no solution?

Back

No solution occurs when the graphs of the equations are parallel and never intersect.

Front

How do you determine the solution of a system graphically?

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

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 feasible region in the context of systems of inequalities?

Back

The area on a graph where all the constraints of the inequalities are satisfied.

Front

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

Back

A point is a solution if it satisfies all equations in the system.

Front

How can you check if a point is a solution to a system?

Back

By substituting the point's coordinates into each equation and verifying if they hold true.