Set Up Systems of Equations + 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 of a system of equations?

Back

A point is a solution if it satisfies all equations in the system.

Front

How do you determine if a point is part of the solution set for a system of equations?

Back

Substitute the point's coordinates into each equation; if all equations are true, the point is part of the solution set.

Front

What is the graphical representation of a system of equations?

Back

The solution is represented by the point(s) where the graphs of the equations intersect.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Front

How do you represent a system of inequalities graphically?

Back

By shading the regions of the graph that satisfy each inequality.

Front

What is the significance of the intersection of shaded regions in a system of inequalities?

Back

The intersection represents the set of solutions that satisfy all inequalities in the system.

Front

What is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are constants.

Front

How can you convert a word problem into a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations based on the problem's context.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that make all equations true simultaneously.