What is the solution of the system of equations? {13x−6y=2 3x−4y=−10

Solve the following system:
{13 x - 6 y = 2 | (equation 1)
{3 x - 4 y = -10 | (equation 2)

Subtract 3/13 × (equation 1) from equation 2:
{13 x - 6 y = 2 | (equation 1)
{0 x - (34 y)/13 = (-136)/13 | (equation 2)

Multiply equation 2 by -13/34:
{13 x - 6 y = 2 | (equation 1)
{0 x+y = 4 | (equation 2)

Add 6 × (equation 2) to equation 1:
{13 x+0 y = 26 | (equation 1)
{0 x+y = 4 | (equation 2)

Divide equation 1 by 13:
{x+0 y = 2 | (equation 1)
{0 x+y = 4 | (equation 2)

Collect results:

  {x = 2                         {y = 4