Solving Pairs of Equations by Substitution
Date: 11/26/97 at 10:46:40 From: Lana Subject: Solving Pairs of equations by substitution I am totally confused by this: 1. x + 3y = - 5 3x - 2y = 7 2. 3s - 4t = 5 s + 7t = 10 3. 3m - n = 15 m + n = 1 4. 2x - 3y = -4 - x - 2y = 7 Please help me. Thanks a lot.
Date: 12/18/97 at 10:50:37 From: Doctor Deanna Subject: Re: Solving Pairs of equations by substitution Hi there :) Help is on the way. This confused me as well when I was first faced with it, but you'll see it's quite easy to understand and perhaps you'll find it a preferred method to solve equations, as I have. Let's look at one of your problems and go through it step by step. 1. x + 3y = - 5 3x - 2y = 7 When you know what x is equal to, solving these equations is much easier. Substitution gives you a way to find x. Take the first equation and solve for x. x + 3y - 3y = -5 - 3y x = -5 - 3y Now you have what you you need: what x is equal to. Next you need to insert it into the second equation. In other words, replace x with (-5 - 3y) just as you would if x were equal to a single number instead of another equation, like this: 3(-5 - 3y) - 2y = 7 Then solve for y doing the necessary computations. You now will have an answer for y that doesn't involve any other variables. You're almost done - just one last step. Take your answer for y and substitute it into either of the original equations (it doesn't matter which one) and solve for x again. This time you will get an answer for x that doesn't contain any variables. Let me know if you need any further help on this but I think this should send you on your way. -Doctor Deanna, The Math Forum :) Check out our web site! http://mathforum.org/dr.math/
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