Question

How is 3x-y=8 and x+2y=5 solved by combination (addition)????? 

Answer 1

First, multiply the first equation by 2.

That turns the first equation into:

6x - 2y = 18

That way it can easily be added to the second equation:

6x - 2y = 16
x  + 2y = 5
---------------
7x = 21
==========

As you can see, the y disappeared, which was the objective of this operation.

Now the equations can be solved easily:

7x = 21
x = 3

Insert x=3 in the original equation:

3*3 - y = 8
9 - y = 8
9 = 8 + y
y = 1

So the result is:

x = 3
y = 1

Answer 2

multiply by 2 =
6x-2y=18
now add
6x - 2y = 16 x  + 2y = 5
---------------
7x = 21
==========
y is gone
now it is easy
7x=21
x=21 divide by 7
x=3
now insert it 
3*3-y=8
9-y=8
9=8+y
y=1  
So the result is:   x = 3 y = 1