Solving EquationsFrom: Anonymous Date: Fri, 28 Jun 1996 9:22:58 -0400 (EDT) Subject: Find k I don't understand this problem. Can you help me? Find k, if 7/x+y = k/x+2 = 11/2-y Date: Fri, 28 Jun 1996 13:33:35 -0400 (EDT) From: Dr. Anthony Subject: Re: Find k If we take first and third of these 7/(x+y) = 11/(2-y) then 14-7y = 11x + 11y or 11x +18y = 14 Now take the 2nd and third expressions to k/(x+2) = 11/(2-y) then 2k - ky = 11x + 22 or 11x + ky = 2k - 22 So we have two equations 11x + ky = 2k-22 and 11x +18y = 14 Subtract (k-18)y = 2k - 36 (k-18)y = 2(k-18) So either y=2 or k = 18. But y=2 puts a zero in the denominator of the last expression, and would require x = -2 and k indeterminate, so we require instead k = 18. Check that this gives first and second expression consistent with first and third. We showed that the first and third led to 11x + 18y = 14, so now try the first and second with k=18 7x + 14 = 18x + 18y 14 = 11x + 18y so the result is consistent. -Doctor Anthony, The Math Forum |
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