Help understanding the system of equations?

Question

I know it'll be by elimination.
2x + y = 5
x + 3y = 0

Answer 1

2x + y = 5-------> (1)

x + 3y = 0

Subtract 3y from each side.

x = -3y

Substitute x = -3y in the equation (1).

2(-3y) + y = 5

-6y + y = 5

- 5y = 5

Divide each side by -5.

y = -1

Substitute y = -1 in the equation (1).

(1) ⇒ 2x - 1 = 5

Add 1 to each side.

2x = 6

Divide each side by 2.

x = 3.

Therefore x = 3. and y = -1.

Answer 2

Multiply the second equation by 2 and subtract from equation 1 to eliminate the variable x.

2x + y = 5

2x + 6y = 0

-----------------

-5y = 5

Divide each side by -5

y = -1

Substitute y = -1 in x + 3y = 0

x - 3 = 0

x = 3

Solution to system of equation is (3, -1)