How do i solve each system by elimination

Solve the following system by elimination:
{6 x + 8 y = -10 | (equation 1)
{y = 3 - 5 x | (equation 2)

Express the system in standard form:
{6 x + 8 y = -10 | (equation 1)
{5 x + y = 3 | (equation 2)

Subtract 5/6 × (equation 1) from equation 2:
{6 x + 8 y = -10 | (equation 1)
{0 x - (17 y)/3 = 34/3 | (equation 2)

Divide equation 1 by 2:
{3 x + 4 y = -5 | (equation 1)
{0 x - (17 y)/3 = 34/3 | (equation 2)

Multiply equation 2 by 3/17:
{3 x + 4 y = -5 | (equation 1)
{0 x - y = 2 | (equation 2)

Multiply equation 2 by -1:
{3 x + 4 y = -5 | (equation 1)
{0 x+y = -2 | (equation 2)

Subtract 4 × (equation 2) from equation 1:
{3 x+0 y = 3 | (equation 1)
{0 x+y = -2 | (equation 2)

Divide equation 1 by 3:
{x+0 y = 1 | (equation 1)
{0 x+y = -2 | (equation 2)

Collect results:

{  {x = 1, y = -2

1) add 8x on both sides
3y=12+8x

2)divide by 3 to solve for y
y=4+8/3x

y=8/3x+4

8/3x is the slope, 4 is the y-intercept