This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1856 edition. Excerpt: ...found to verify. This method of eliminating, as it is called, one of the unknown quantities, and so reducing the two equations to one of one unknown quantity, is sufficient for the solution of any pair of equations of the above form which hold true When Equations are bracketed in this way it is meant ...
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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1856 edition. Excerpt: ...found to verify. This method of eliminating, as it is called, one of the unknown quantities, and so reducing the two equations to one of one unknown quantity, is sufficient for the solution of any pair of equations of the above form which hold true When Equations are bracketed in this way it is meant that they hold true for the same values of the unknown quantities. They are sometimes called Simultaneous Equations. 2itf = 25-3x = 25-21 = 4, .-. y = = 2. The methods here employed may obviously be applied to all other like cases, where two distinct equations are given, either in the above form, or capable by previous rules of being reduced to that form: --the general object being so to frame one equation out of the two, that one of the unknown quantities shall be made to disappear. The most usual method is that employed in the last case; and the rule is--Mark which of the unknown quantities has the least coefficients, (so as to make the easiest multipliers), and supposing it to be y, multiply the 1st equation by the coefficient of y in the 2nd, and the 2nd equation by the coefficient of y There are some cases, however, in which the preceding Rule should not be strictly applied, especially if the numerical quantities in the equations are large. For example, Ex.1. If l6r + 23y = 94, ), and 14-12 = 18, J J Here 112 is the Least Com. Mult. of 16 and 14, and it contains the former 7 times and the latter 8 times;.. multiplying the 1st equation by 7, and the 2nd by 8, we have PROBLEMS; DEPENDING UPON THE SOLUTION OF SIMPLE EQUATIONS OP TWO UNKNOWN QUANTITIES. Phob. 1. The sum of two numbers is 26, and, if the half of the greater of them be added to the third part of the other, the sum of these parts is 11. What are the numbers? Let x and y..
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