systems of equations and inequalities review

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 if a system of equations has no solution?

Back

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

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, resulting in an infinite number of intersection points.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the graphical representation of a linear inequality?

Back

It is represented by a line (solid or dashed) and a shaded region indicating the solution set.

Front

What does a solid line indicate in a linear inequality?

Back

It indicates that the points on the line are included in the solution set (≥ or ≤).

Front

What does a dashed line indicate in a linear inequality?

Back

It indicates that the points on the line are not included in the solution set (> or <).

Front

How can you determine the cost of items using a system of equations?

Back

By setting up equations based on the total cost and quantities of items, then solving the system.

Front

What is the first step in solving a system of equations by elimination?

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

What is the purpose of graphing a system of equations?

Back

To visually identify the point(s) of intersection, which represent the solution(s) to the system.