Date: Sun, 15 Nov 1998 17:26:15 -0500
Subject: I have a question

My name is Crystal.Im in grade 11. I have a question.We are solving linear systems of equations: comparison method. My questions is. it says

a)use the method of comparison to solve this system a=b-1, 3a+ b=3

b) verify your solutin in a

I dont understand it. please help

Thank you

Dear Crystal
The method of comparison means that you compare two different ways of writing something equal to a or something equal to b. Since a = b -1 and 3a + b = 3 we can compare the two different ways of writing something equal to b.
  From the first equation we can see that a + 1 = b and so b = a + 1. From the second equation we can see that b = 3 - 3a. Since b = b then we can say that a + 1 = 3 - 3a and so a + 3a = 3 -1 and so 4a = 2 and so a = 1/2. But since, in the first equation b = a + 1 then b = 1/2 + 1 = 3/2 And so a = 1/2 and b = 3/2.
  To verify you need to use the values for a and b and substitute them into the Left Side and Right Side of each of the original equations to see if the Left Side = the Right Side in both equations. It is important that you use the original equations to verify in case you make a mistake in going from the original equations to the equations that were in the form b = .....
  You will notice that we could have done the original question by getting equations in the form a = .... and then comparing them. We did not do this because it involved fractions. The method is OK but it increases your chance of error because you would be dealing with a = b -1 and a = (3 - b)/3 and so b - 1 = (3 - b)/3, etc.

I hope that this helps.

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