Gradations in Algebra; In Which the First Principles of Analysis Are Inductively Explained

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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. 1850 edition. Excerpt: ... make the term which contains that unknown quantity to be the same in both. Then if the identical terms have Like signs in both equations, Subtract one equation from the other; but if they have Unlike signs, Add one equation to the other. And the result will be an equation containing only one unknown quantity. Questions. What is the first operation for exterminating an unknown quantity Repeat the whole rule. What are identical terms? Why do we add them when the signs are unlike? Why do we subrati them when the signs are alike? EQUATIONS.--SECTION 11. 1. What two numbers are those whose sum is 20 and dif ference 12? Stating the question, X= greater number. y = the less. Then forming the equations, x+y = 20 As the signs of the identical terms are unlike, add the equations, ' Substituting 16 for a; in the first, 16+y = 20 Transposing and uniting, y = 4. Ans. 16 and 4. 2. A market woman sells to. one person, 3 quinces and 4 melons for 25 cents; and to another, 4 quinces and 2 melons, at the same rate, for 20 cents. How much are the quinces and melons apiece? After the statement, forming the 3a;+4y = 25 equations, 5 4af+2i/ = 20 Multiplying the second by 2, 8a;+4t/ == 40 Subtracting first from third, 5x =15 Ans. Quinces, 3 cents apiece; melons, 4. In our solutions after this, we shall number the lines, so that any reference to them will be easily understood. 3. A man bought 3 bushels of wheat and 5 bushels of rye for 38 shillings; and at another time, 6 bushels of wheat and 3 bushels of rye for 48 shillings. What was the price for a bushel of each? Let x = price of wheat, and y = price of rye. 1. By the first condition, 3x + 5/ = 38 2. By the second, 6x + 3y = 48 3. Multiply the 1st by 2, 6x+ Wy = 76 4. Subtracting the 2d from the 3d, 7i/...show more

Product details

• Paperback | 42 pages
• 189 x 246 x 2mm | 95g
• English
• Illustrations, black and white
• 1236840720
• 9781236840721