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multiply the first equation by 3 , then add them together...

So when you do that then add the two together, a variable goes to zero and drops out

14x = -29

Here i will do each basic step for this example.....

4x - 1y = -11
2x + 3y = 5
If added together, you just will get 6x + 2y = -6

you see that so far?

if you multiply the first by 3, you will have a -3y in the first and a +3y in the second

you see what i mean ?

no, lets continue....

sorry
12x - 3y = -33
2x + 3y = 5
------------------

now add them together, both sides of the equals

14x=28!

Multiplying an equation by a constant number, and
Adding two equations together...
that is it

I could type all the dumb script rules in, but those are the ideas

One step further.....

Say you have one that has terms on the Y like this
... 3y = 10
... 2y = 41

How to get those to add and cancel out...
multiply the first by +2
Multiply the second by -3

6y
-6y
-----
0y

just take care of the X and right side of the = when you multiply through and add too

That is it... good luck

welcome, practice.. hehe