Systems of Equations and Inequalities Final Review

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 point(s) where the equations intersect.

Front

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

Back

A point of intersection is where the graphs of the equations meet, representing the values of the variables that satisfy all equations in the system.

Front

Define a linear inequality.

Back

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane divided by a line. The line represents the boundary, and the shaded area indicates the solutions.

Front

How do you solve a system of equations using substitution?

Back

To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation to find the second variable.

Front

What is the elimination method for solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

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

Back

A consistent system has at least one solution. It can be either independent (one solution) or dependent (infinitely many solutions).

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the lines represented by the equations are parallel and never intersect.

Front

How can you represent a real-world problem as a system of equations?

Back

Identify the variables, write equations based on the relationships described in the problem, and ensure the equations reflect the constraints and conditions given.

Front

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

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables. A positive slope means an increasing relationship, while a negative slope indicates a decreasing relationship.