How do I solve an elimination problem when the one of the coeficcint's is on the other side of the equal sign?

Question

-3+3y=6x

-10x+6y=4

Answer 1

First equation  : - 3 + 3y = 6x              ----------------(1)

Second equation : - 10x + 6y = 4             ----------------(2)

(1)  ⇒   3y = 6x + 3             ----------------(3)

Multiply with 2 both sides.

2(3y) = 2(6x + 3)

6y = 12x + 6.

Substitute 6y value in Second equation.

-10x + 6y = 4   ⇒   -10x + (12x + 6) = 4

2x + 6 = 4

Add - 6 to each side.

2x + 6 - 6 = 4 - 6

2x  = - 2

Divide each side by 2.

2x/2  = - 2/2

x = - 1.

 

Substitute x = - 1 in equation (3).

3y = 6x + 3  ⇒  3y = 6(-1) + 3

3y = - 6 + 3

3y = - 3

Divide each side by 3.

3y/3 = - 3/3

y = -1.

Solution : x = -1 , y = -1.