Solve each system by substitution. Determine whether each system is independent, inconsistent, o

step 1 We're asked to solve this system by substitution. X plus Y equals 1 and 2x minus 3Y equals 8. So

Solve each system by substitution. Determine whether each...

Key Concepts

Dependent System

A dependent system has infinitely many solutions, which occurs when the equations in the system are essentially the same line (one equation can be transformed into the other). This means that every solution of one equation is also a solution of the other.

Inconsistent System

An inconsistent system of equations does not have any solution because the equations represent lines that are parallel. Since parallel lines never intersect, there's no point that satisfies all equations simultaneously.

Independent System

An independent system is a set of equations that has exactly one unique solution. In the context of two linear equations, this means that the lines represented by the equations intersect at a single point, indicating that the equations are distinct and not multiples of each other.

Substitution Method

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation(s). This technique simplifies the system by reducing the number of variables in each equation, ultimately leading to a single equation that can be solved directly.

System of Linear Equations

A system of linear equations consists of two or more equations with the same set of unknowns, and the goal is to find the values of these unknowns that satisfy all the equations at the same time. These systems form the basis of solving problems in algebra and are applicable in various fields like physics, economics, and engineering.

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