12x+5y==13
-24x-5y=-11
-2x+4y=32
-5x-10y=-20
12x+12y=36
-8x-8y=-8
solve and explain

12x+5y=13 is y=13/5-12/5x
-24y-5y=-11 is y=-11/-5+(24/-5)x

-2x+4y=32 is y=32/4+2/4x
-5x-10y=-20 is y= -20/-10+(5/-10)x

12x+12y=36 is y=36/12-12/12x
-8x-8y=-8 is y=-8/-8+(8/-8)x

1. 12x + 5y = 13
-24x - 5y = -11

First Add these equations to cancel out the y value so we can find the x value.
(12x + 5y = 13) + (-24x - 5y = -11) 
= -12x + 0y = 2
Now we are left with the equation -12x = 2
Next divide both sides by -12 and x = -1/6
Now plug x into any of the original two equations to find the y-value.

12(-1/6) + 5y = 13
-2 + 5y = 13
5y = 15
y = 3

or 
-24(-1/6) - 5y = -11
4 - 5y = -11
-5y = -15 
y = 3

Sp, x = -1/6 and y = 3

2.-2x + 4y = 32
   -5x - 10y = -20

First, lets simplify both of the equations.

(-2x + 4y = 32) / -2 = x - 2y = -16
(-5x - 10y = -20) / -5 = x + 2y = 4

Now we have the two equations:

x - 2y = -16
x + 2y = 4

Subtract the equations from each other to cancel out the 'x'.
(x - 2y = -16) - (x + 2y = 4)
 = -4y = -20 

-4y = -20 
Divide by -4
y = 5

Now plug 5 in for y in the equations:

x - 2y = -16
x + 2y = 4

x - 10 = -16
x = -6

x + 10 = 4
x = -6

So , y = 5, and x = -6

3. 12x + 12y = 36
-8x - 8y = -8

Lets also simplify the equations.

(12x + 12y = 36) / 12 =   x + y = 3
(-8x - 8y = -8) / -8 = x - y = 1

Right off the bat you can say that x = 2 and y = 1.

2 + 1 =3
2 - 1 = 1

But mathematically:

Subtract both equations

(x + y = 3) - (x - y = 1) 
= 2y  =  2

2y = 2
y = 1

x + 1 = 3
x = 2

x - 1 = 1
x = 2

So x = 2 and y = 1;