how do I Solve using the elimination method ?

Solve the following system:
{5 y = 4 x+3 |     (equation 1)
2 x+6 y = -6 |     (equation 2)
Express the system in standard form:
{-(4 x)+5 y = 3 |     (equation 1)
2 x+6 y = -6 |     (equation 2)
Add 1/2 × (equation 1) to equation 2:
{-(4 x)+5 y = 3 |     (equation 1)
0 x+(17 y)/2 = (-9)/2 |     (equation 2)
Multiply equation 2 by 2:
{-(4 x)+5 y = 3 |     (equation 1)
0 x+17 y = -9 |     (equation 2)
Divide equation 2 by 17:
{-(4 x)+5 y = 3 |     (equation 1)
0 x+y = (-9)/17 |     (equation 2)
Subtract 5 × (equation 2) from equation 1:
{-(4 x)+0 y = 96/17 |     (equation 1)
0 x+y = -9/17 |     (equation 2)
Divide equation 1 by -4:
{x+0 y = (-24)/17 |     (equation 1)
0 x+y = -9/17 |     (equation 2)
Collect results:
Answer: | {x = -24/17         and            y = -9/17
 

5y=4x+3        transform this to                -4x + 5y  =  3    (1)

2x+6y= -6      multiply through by 2         4x + 12y  = -12    (2)

Add  (1)   and (2)    ....     this gives us

17y = -9       divide both sides by 17

y = -9 / 17

And using ( 1),   we can find x as :

-4x + 5 ( -9 / 17)  =  3

-4x - 45/17  = 51 / 17       add    45/17 to both sides

-4x  = 96/17                    divide both sides by -4

x = -24 / 17