Is there an specific order for solving systems of equations when doing substitutions?

[Mathmonkey]

I don't have a math problem right now, but whenever I'm given a system of equations, I get different answers depending on the order in which I solve them. This issue has been following me since 8th grade. I think I'm messing up the steps as I solve them. Do you guys have any method you use to determine the order in which you solve them? Anything will help.

 

[mmm4444bot]

Is there an specific order for solving systems of equations when doing substitutions?

No, but some choices may be more natural than others. It depends on the system.

… whenever I'm given a system of equations, I get different answers depending on the order in which I solve them.

It sounds like you might be making mistakes. Some of those answers could have been correct.

… I think I'm messing up the steps as I solve them.

Let's see how it goes. Please show your work on solving the following system of equations, using the substitution method.

5y + 13 = 8x

4x + 5y/3 = 9

 

[Ishuda]

I don't have a math problem right now, but whenever I'm given a system of equations, I get different answers depending on the order in which I solve them. This issue has been following me since 8th grade. I think I'm messing up the steps as I solve them. Do you guys have any method you use to determine the order in which you solve them? Anything will help.

If the number of equations is small (say 3 or less), I generally do a direct substitution unless it appears something is easier. A very simple example whose solution should be causal to the more simple observer:
(1) x + y = 7
(2) x - y = 1
so
(1') x = 7 - y
(2') (7-y) -y = 1 or 6=2y or y=3

(1'') x = 7 - y = 7 - 3 = 4


Otherwise just go through the usual augmented matrix and row reduction method. An example of this for a 3X3 system is shown at
http://www.mathportal.org/algebra/solving-system-of-linear-equations/row-reduction-method.php

 

[mmm4444bot]

Wouldn't you simply add the 2 equations …

Not if you were instructed to use substitution. This thread is about substitution methods.