Math..linear equation..PLEASE HELP :(

The first equation has a 2x.
The second equation has a 6x.
If you multiply 2x by -3, then add the product to 6x, the result is zero. That means you have eliminated the x variables.
:::::
2x - y = 13
Multiply the equation by 6 to get
12x - 6y = 78

6x + 4y = 4
Multiply the equation by -2 to get
-12x - 8y = -8

Add the new equations together:
12x - 6y = 78
-12x - 8y = -8
--------------------
-14y = 70

solve for y: y = -70/14 = -5

plug the value of y into the first equation and solve for x:
2x - (-5) = 13
2x = 8
x = 4

2x - y =13 ............(i)
6x+4y=4 .............(ii)
To eliminate y multiply (i) by 4 and add to (ii)
(8x - 4y)+ (6x +4y) = 52 +4=56
14x = 56
x = 4.............(iii)
from (i)
2*4 - y = 13
y = 8 -13 = -5 ............(iv)
Hence x= 4 and y =-5 ............Ans

First when you multiply an entire equation by a constant, in your case a 2, it does not change the solution to that equation. For example the following easy equation

2x = 4
x = 2

now multiply entire equation by 2

4x = 8
x = 2

What you are looking for is the easiest way to manipulate one of the equations so that we you add them one of the variables drops out. In effect finding the negative coefficient of one of the variables. So in your case we notice that the x values have the same sign. However, 6 is a multiple of 3, namely 2 and since our goal is to find the negative we multiply by not 3 but - 3 and get the following system.

- 6x + 3y = - 39
6x + 4y = 4

not add the two equations and we get

7y = - 35

solve for y and we get

y = - 5

now replace y with - 5 in one of the original equations and solve for x

2x - (- 5) = 13

2x + 5 = 13

2x = 8

x = 4

so solution is (4, - 5)