Systems of Equations and Inequalities

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 solution to a system of equations to be consistent?

Back

A consistent system has at least one solution.

Front

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

Back

An inconsistent system has no solutions.

Front

What is the graphical representation of a system of inequalities?

Back

The solution is represented by the shaded region where the inequalities overlap.

Front

What is substitution in solving systems of equations?

Back

Substitution involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is elimination in solving systems of equations?

Back

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

Front

What is the solution to the system of equations 2x + 3y = 6 and x - y = 1?

Back

(3, 0) is the solution.

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

Parallel lines have the same slope and will never intersect, indicating no solution for the system.

Front

What is the meaning of 'no solution' in a system of equations?

Back

It means that the equations represent lines that do not intersect.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the point into each inequality; if it satisfies all inequalities, it is a solution.