Substitution method?

Question

x-2y=0 & 3x=y How do you do this one? How do you know what to do, when one equation needs to be solved first, how do you know which one?

Answer 1

You pick one: you find the value of one variable, relative to the other:

x - 2y = 0
x = 2y

We have found the value of x, relative to y.

We go to the second equation and substitute the value of x we have just found:

3x = y
3(2y) = y
6y = y

Therefore y = 0 (it is the only value that allows you to have 6y = y

Back to the furst one:
x = 2y
Therefore, x = 0 as well.

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It does not matter which one you do first. However, in some problems, there may be one that is easier to do than the other, so you start with the easy one.

Answer 2

Hmm, I wouldn't say you solve an equation first. It is just which side (x or y) you solve first.

x-2y=0 --- (1)
3x=y --- (2)

In this case, you can take y to substitute in since it is so nicely given that y=3x. You usually take the one that does not have a number attached.

taking equation (2), sub into (1)
x-2(3x)=0
x-6x=0
-5x=0
x=0

sub x=0 into (1)

0-2y=0
2y=0
y=0

The answers are a bit weird, I don't know if something went wrong somewhere. Or maybe I usually don't get such answers so I find them weird...

But generally for such equations:

1. if you use substitution, take the ones that are for example 5x=y and not those that are 5y+8=x to substitute into the other
2. if you use elimination, you usually blow up the smaller number but this method is more prone to error.

Hope this helps.

Answer 3

You have linear equations in two unknowns, i.e., x and y.
If you want to solve these equations by substitution you have to express first one of the variables in terms of the other variable. Say, for this problem, let us express y in terms of x. You choose which of the two equations you want to use in order to express y in terms of x. Your given equations are both simple and any one of them can be used. However, in other cases, you may have to choose wisely--choose the equation that is simpler, one that won't be very difficult to transform to the chosen variable.

Choose----- 3x = y
Substitute in the other equation:
x - 2y = 0
x - 2(3x) = 0
x - 6x = 0
-5x = 0
x = 0/(-5)
x = 0
Therefore, by 3x = y
y = 3(0)
y = 0

teddyboy

Answer 4

im pretty sure i learned this in like 6th or 7th grade.
soo i might not remember...

it doesn't matter which equation is solved first. you just have to pick a variable and isolate it
like...
3x=y; you divide both sides by 3 so x can be by itself.
x=y/3
now you take the other equation and plug that in for x...
it looks like this...
(y/3)-2y=0
now you solve for y.....
and so on.


i hope this helps.
i dont know if im even doing the right type of math.

Answer 5

You can use any one of them. Doesn't make a difference as eventually you get both x and y = 0.

Answer 6

x-2y=0 & 3x=y
x=2y & 3x=y
So this question cannot be answered.

Answer 7

x - 6x = 0
- 5x = 0
x = 0
y = 0