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.

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What does it mean for a system of equations to have infinitely many solutions?

Back

It means that there are an infinite number of points that satisfy all equations in the system.

Front

What is a solution to a system of equations?

Back

A set of values for the variables that makes all equations in the system true.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines or curves representing the equations.

Front

What does it mean if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

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 satisfied, it is a solution.

Front

What is a system of inequalities?

Back

A set of two or more inequalities that are solved together.

Front

How do you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane and identify the region where all inequalities overlap.

Front

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

Back

The point must satisfy all inequalities in the system.

Front

What is the difference between a solution and a feasible solution in a system of inequalities?

Back

A solution satisfies the equations, while a feasible solution satisfies the inequalities.