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

How do you represent a system of equations graphically?

Back

Graphically, a system of equations is represented by the lines of the equations on a coordinate plane. The point(s) where the lines intersect represent the solution(s) to the system.

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

Back

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

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.

Front

How do you solve a system of equations using elimination?

Back

To solve by elimination, manipulate the equations to eliminate one variable, allowing you to solve for the other variable.

Front

What is the graphical representation of the inequality y < mx + b?

Back

The graph of y < mx + b is a dashed line representing the boundary, with the solution set being the area below the line.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates they are not included (> or <).

Front

What does the solution set of a system of inequalities represent?

Back

The solution set of a system of inequalities represents all the points that satisfy all inequalities in the system, often depicted as a shaded region on a graph.

Front

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

Back

To check if a point is a solution, substitute the point's coordinates into each inequality. If it satisfies all inequalities, it is a solution.