Y=5x+2 and 3x=-y+10 what is the soluion of equation

Solve the following system:

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

{-(5 x) + y = 2 | (equation 1)
{3 x + y = 10 | (equation 2)

Add 3/5 × (equation 1) to equation 2:
{-(5 x) + y = 2 | (equation 1)
{0 x+(8 y)/5 = 56/5 | (equation 2)

Multiply equation 2 by 5/8:
{-(5 x) + y = 2 | (equation 1)
{0 x+y = 7 | (equation 2)

Subtract equation 2 from equation 1:
{-(5 x)+0 y = -5 | (equation 1)
{0 x+y = 7 | (equation 2)

Divide equation 1 by -5:
{x+0 y = 1 | (equation 1)
{0 x+y = 7 | (equation 2)

Collect results:
  {x = 1                         {y = 7