5y+3x=13/2

y=-5x+57/10 steps

Express the system in standard form:

{3 x + 5 y = 13/2 | (equation 1)

{5 x + y = 57/10 | (equation 2)

Swap equation 1 with equation 2:

{5 x + y = 57/10 | (equation 1)

{3 x + 5 y = 13/2 | (equation 2)

Subtract 3/5 * (equation 1) from equation 2:

{5 x + y = 57/10 | (equation 1)

{0 x + (22 y) / 5 = 77/25 | (equation 2)

Multiply equation 1 by 10:

{50 x + 10 y = 57 | (equation 1)

{0 x + (22 y) / 5 = 77/25 | (equation 2)

Multiply equation 2 by 25/11:

{50 x + 10 y = 57 | (equation 1)

{0 x+10 y = 7 | (equation 2)

Divide equation 2 by 10:

{50 x + 10 y = 57 | (equation 1)

{0 x+y = 7/10 | (equation 2)

Subtract 10 * (equation 2) from equation 1:

{50 x+0 y = 50 | (equation 1)

{0 x+y = 7/10 | (equation 2)

Divide equation 1 by 50:

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

{0 x+y = 7/10 | (equation 2)

Collect results:

Answer: {x = 1

{y = 7/10