I've tried elimination of every type and its required, but 2x+6y=18 and 3x+2y=13

Lets start with one of the equations. 

2x+6y=18

Add -6y to both sides.

2x+6y+−6y=18+−6y

2x=−6y+18

Divide both sides by 2.

2x2=−6y+182

x = −3y + 9 <--

Now lets plug this into the other equation.

Simplify both sides of the equation.

3(−3y+9)+2y=13

Simplify

−7y+27=13

Subtract 27 from both sides.

−7y+27−27=13−27

−7y=−14

Divide both sides by -7.

−7y/−7 = −14/−7

y=2


y=2
Now that we figured out the value for y, lets plug it into either equation. 

2x+6(-2)=18

Simplify both sides of the equation.

2x+(6)(−2)=18

Simplify

2x−12=18

Add 12 to both sides.

2x−12+12=18+12

2x=30

Divide both sides by 2.

2x/2 = 30/2

x=15
Final  

y = 2 
x = 15

Google it that might work