Systems of Word Problems 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 represent a word problem as a system of equations?

Back

Identify variables for the unknowns, translate the problem into equations based on relationships described.

Front

What is an inequality?

Back

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

Front

How can you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane and identify the overlapping region as the solution set.

Front

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

Back

A feasible solution is one that satisfies all constraints represented by the inequalities.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the point into each inequality; if it satisfies all, it is a solution.

Front

What is the graphical representation of a linear inequality?

Back

A linear inequality is represented by a shaded region on one side of the line, indicating all possible solutions.