2x - 3y + 13 = 0

3x - 2y + 12 = 0

x = - 2, y = 3

Step-by-step explanation:

Solve the following system:

{13 + 2 x - 3 y = 0 | (equation 1)

12 + 3 x - 2 y = 0 | (equation 2)

Express the system in standard form:

{2 x - 3 y = - 13 | (equation 1)

3 x - 2 y = - 12 | (equation 2)

Swap equation 1 with equation 2:

{3 x - 2 y = - 12 | (equation 1)

2 x - 3 y = - 13 | (equation 2)

Subtract 2/3 * (equation 1) from equation 2:

{3 x - 2 y = - 12 | (equation 1)

0 x - (5 y) / 3 = - 5 | (equation 2)

Multiply equation 2 by - 3/5:

{3 x - 2 y = - 12 | (equation 1)

0 x+y = 3 | (equation 2)

Add 2 * (equation 2) to equation 1:

{3 x+0 y = - 6 | (equation 1)

0 x+y = 3 | (equation 2)

Divide equation 1 by 3:

{x+0 y = - 2 | (equation 1)

0 x+y = 3 | (equation 2)

Collect results:

Answer: {x = - 2, y = 3