# Systems of Equations - Unknowns And Linear Equations, Solutions Of Linear Equations, Systems In Three Or More Variables

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Systems of equations are a **group** of relationships between various unknown variables which can be expressed in terms of algebraic expressions. The solutions for a simple system of equation can be obtained by graphing, substitution, and elimination addition. These methods became too cumbersome to be used for more complex systems however, and a method involving matrices is used to find solutions. Systems of equations have played an important part in the development of business and quicker methods for solutions continue to be explored.

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Many times, mathematical problems involve relationships between two variables. For example, the distance that a car moving 55 mph travels in a unit of time can be described by the equation y = 55x. In this case, y is the distance traveled, x is the time and the equation is known as a linear equation in two variables. Note that for every value of x, there is a value of y which makes the equation tr…

Since the previous age problem represents a system with two equations and two unknowns, it is called a system in two variables. Typically, three methods are used for determining the solutions for a system in two variables, including graphical, substitution and elimination. By graphing the lines formed by each of the linear equations in the system, the solution to the age problem could have been ob…

Systems of equations with more than two variables are possible. A linear equation in three variables could be represented by the equation ax + by + cz = k, where a, b, c, and k are constants and x, y, and z are variables. For these systems, the solution set would contain all the number triplets which make the equation true. To obtain the solution to any system of equations, the number of unknowns …

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