Text-Book of Algebra Volume 1; With Exercises for Secondary Schools and Colleges (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1898 Excerpt: ...we can assign to x any value whatever, i.e., the problem is indeterminate. Solving this equation as a linear equation, we obtain x-x = 40-40, or (1-l)x = 40-40; 40-40 0 whence x = =--1-1 0 The indeterminate result, -, therefore means that any finite number satisfies the condition of the problem. It is evident from the problem that the father will be at any time 30 years older than his son. Pr. 2. A merchant buys 4 pieces of goods. In the second there are 3 yards less than in the first, in the third 7 yards less than in the first, and in the fourth 10 yards less than in the first. The number of yards in the first and fourth is equal to the number of yards in the second and third. How many yards are there in the first piece? Let x = the number of yards in the first piece, then x--3 = the number of yards in the second piece, x--7 = the number of yards in the third piece, x--10 = the number of yards in the fourth piece. Therefore, by the condition of the problem, we have x ](x-10) = (a;-3) + (x-7), or 2x-10 = 2x-10. This equation is an identity, and is therefore satisfied by any finite value of x. If it be solved in the usual way, we obtain (2-2) x = 10-10, 10-10 0 That is, the conditions of the problem will be satisfied by any number of yards in the first piece. Infinite Solutions. n Pr. 1. What number must be added to the numerator and denominator of $ to give 1? Let i stand for the required number. Then, by the condition of the problem, we have 2 + x = 1 6 + x' or 2 + x = 5 + x. Evidently no finite value of x will satisfy this equation, since 2 plus any finite number cannot be equal to 5 plus the same finite number. But if the equation be solved as a linear equation, we obtain x--x = 6--2, (1-l)x = 5-2; 5-2 8 whence The meaning of this result is, that the gre...