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Substituting these values in (1) and (2), we have

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4Q

(5).

9

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If we take the minus sign in the second member of equation

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Whence, by combining (1) and (6) as in the 3d example,

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300. For examples of more than two unknown quantities, no additional illustrations are necessary. The few cases which lead to a final equation in the quadratic form are to be treated by the same methods that apply to the preceding. And skill in the management of this whole class of examples, must depend less upon precept than upon practice.

301. As auxiliary to the solution of certain questions, particularly in geometrical progression, we give the following

PROBLEM.-Given x + y =s and xy = p, to find the values of x2+ y2, x3+y3, x1+y1, and 25+y3, expressed in terms of s and p.

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The following example will illustrate the use of these formulas.

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If we take xy = 148, the values of x and y will be imaginary. Taking xy 14, with the equation x+y=9, we readily obtain

=

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EXAMPLES

OF

SIMULTANEOUS EQUATIONS.

Find the values of the unknown quantities in the following groups of equations:

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