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# What is the history of linear equations?

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Linear algebra originated as the study of linear equations and the relationship between a number of variables. Linear algebra specifically studies the solution of simultaneous linear equations.

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A linear equation is defined as a mathematical concept in which no variable is multiplied by itself or any other variable. For instance, the equation 4x + 2y - z = 0 is a linear equation in three variables, while the equation 2x - y = 7 is a linear equation in two variables. From linear algebra emerges two important concepts: vectors and matrices. The vector corresponds to directed line segments, and the matrix finds the coefficients of a simultaneous equation.

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Everyday budgeting and other financial issues often use linear equations. Linear equations involve two values that change according to a consistent pattern.

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Real-life examples of linear equations include distance and rate problems, pricing problems, calculating dimensions and mixing different percentages of solutions. One application of linear equations is illustrated in finding the time it takes for two cars moving toward each other at different speeds to reach the same point. Another example is estimating how much a shirt on sale for \$20 and marked down by 35 percent cost before the sale.

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Math formulas are used to define relationships between a number of variables. Although math formulas can be expressed in the form of equations, not all equations are math formulas. The variables in an equation are denoted by symbols such as "X" or "Y", which represent values not already known. For example, the math formula for working out the volume of a cube, or box, is given by V= lwh.