Three Simultaneous EquationsDate: 4/16/96 at 8:32:41 From: Anonymous Subject: three variables in three equations I am stuck on this equation. Can you help me solve the problems? -20x + 7y - z = 4 4x - 2y + 24z = 2 7y - 3z + 21y = 7 Date: 4/17/96 at 14:21:8 From: Doctor Sebastien Subject: Re: three variables in three equations Hello, The trick to solve this type of problem is to reduce the equations to 2 unknowns. Let's name the equations: -20x + 7y - z = 4 ----(1) 4x - 2y + 24z = 2 ----(2) 7x - 3y + 21z = 7 ----(3) You will need to check this equation. I assume that this is what you meant. Multiply the (1) by 24 and add it to (2). We get -476x + 166y = 98 ----(4) That gets rid of a z. Multiply (2) by -7/8 and (3) by 8/7 and add them together. We get (9/2)x - (47/28)y = 25/4 ---(5) You now have 2 equations with 2 unknowns, which should be easy to solve. You can then substitute back the values you have for x and y into any of the original equations to get z. -Doctor Sebastien, The Math Forum |
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