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 do you graph a system of equations?

Back

Graph each equation on the same coordinate plane and identify the point(s) where they intersect.

Front

What is the substitution method for solving systems of equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

Add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

Front

How do you graph a linear inequality?

Back

Graph the corresponding equation as a line, then shade the region that satisfies the inequality.

Front

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

Back

A system of inequalities is consistent if there is at least one solution that satisfies all inequalities.

Front

What is the difference between a solution to an equation and a solution to an inequality?

Back

A solution to an equation is a specific point, while a solution to an inequality is a range of values.

Front

What is the feasible region in a system of inequalities?

Back

The feasible region is the area on the graph where all inequalities overlap, representing all possible solutions.