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.

2x 2 = - 6y + 18 2

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

Answer:

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 answer:

y = 2

x = 15