1902-10-01 10.2307/j100069 10 220 10.2307/j100069 220 1902 10.2307/2968881 amermathmont 156 220 156. Proposed by B. F. FINKEL, A.M., M.Sc., Professor of Mathematics and Physics, Drury College,Spring- field, Mo. (z+x)a-(z-x)bz_2yz .... (1); (x+y)b-(x-y)c_2xz .... (2); (y+z)c- (y-z)a=2xy....(3). Find the values of x, y, and z by the method of linear si- multaneous equations. Solution by G. B. M. ZERR, A.M., Ph. D., Professor of Chemistry and Physics, The Temple College, Philadel- phia, Pa. Let x=4(b+c)u, yz4(a+c)v, z=j(a+b)w. (a-b)w+(b+c)u-(a+c)vw....(1). (b-c)u+(a+c)v-(a+b)uw.... (2). (c-a)v +(a +b)w-(b -+c)uv .... (3) . We might eliminate v, w and get an equation of the fifth degree in u. We will, however, proceed as follows: Add (1), (2), (3), then aw(2-u-v) +bu(2-v-w) tev(2-u-w)==O. This is the ease when u v w=O; or u=v--w 1; or u=O, w=-v-2; or v=O, u_-w=2; w O, u v=2. The first two sets of values satisfy the conditions. x=y=z=O; x=j(b+c), y=4(a4-c), z=4(a+b). NOTE. This is exercise 31, page 224, Systems of Linear simultaneous Equations, of Fisher and Schwatt's Higher Algebra, and has given teachers of algebra throughout the country considerable trouble. Solving the equations for a, b, and c, we readily find that a=-x ++z, b=x-y+z, and c=x:+y-z . .. x=&(b+c), i=&(a+c), z=&(a+b), as one set of values for x, y, and z. EDITOR F. Also solved by L. C. WALKER. xml-10 p-10 eng 10 Oct., 1902 The American Mathematical Monthly 9 Finkel B. F. Zerr G. B. M. 1 10.2307/i349203 research-article 00029890