In the previous chapters we have discussed equations involving one variable quantity, for example x or y, a or b, etc., and equations involving two variable quantities, for example x and y, a and b, etc. The first kind was discussed in the section entitled simple linear equations, the second in the section entitled simultaneous linear equations. Before considering the meaning and purpose of a graph in engineering let us briefly re-examine the words ‘linear’ and ‘simultaneous’ as used above. Linear means that the power to which the variable or variables are raised throughout is unity, that is equations containing x2, y2, x3, etc. are not linear equations. The reason for the use of the word linear will become apparent in this chapter. Simultaneous used in the mathematical context means that the equations given are valid at the same time. This simply means that for two such equations involving two unknowns (or three such equations involving three unknowns, etc.) there is only one value of each variable which satisfies all the equations simultaneously. (This applies equally to one equation containing only one variable, but there is then no need for the use of the word ‘simultaneous’.)
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