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

$\begin{cases} 3x-y=8 \ \ / \cdot 2 \\ x+2y=5 \end{cases} \\\\ \begin{cases} 6x-2y=16 \\ x+2y=5 \end{cases} \\+--------\\7x=21 \ \ / :7\\\\x=3$

$x+2y=5\\ \\ 3+2y=5 \\\\2y=5-3\\\\2y=2\ \ / :2\\\\y=1\\\\ \begin{cases} x=3 \\ y=1 \end{cases}$