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 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 determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if all equations are true, it is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

What does it mean if two lines intersect in a graph of a system of equations?

Back

It means there is a unique solution to the system at the point of intersection.

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means there is no solution to the system, as the lines never intersect.

Front

What does it mean if two lines coincide in a system of equations?

Back

It means there are infinitely many solutions, as the lines are the same.

Front

What is an inequality in the context of systems?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or equal to the other.

Front

How do you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane and shade the region that satisfies all inequalities.

Front

What is the solution set of a system of inequalities?

Back

The set of all points that satisfy all inequalities in the system.