3a + 4b = 2

5a + 9b = 1

Solve the following system using elimination:

{3 a + 4 b = 2 | (equation 1)

{5 a + 9 b = 1 | (equation 2)

Swap equation 1 with equation 2:

{5 a + 9 b = 1 | (equation 1)

{3 a + 4 b = 2 | (equation 2)

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

{5 a + 9 b = 1 | (equation 1)

{0 a - (7 b) / 5 = 7/5 | (equation 2)

Multiply equation 2 by 5/7:

{5 a + 9 b = 1 | (equation 1)

{0 a - b = 1 | (equation 2)

Multiply equation 2 by - 1:

{5 a + 9 b = 1 | (equation 1)

{0 a+b = - 1 | (equation 2)

Subtract 9 * (equation 2) from equation 1:

{5 a+0 b = 10 | (equation 1)

{0 a+b = - 1 | (equation 2)

Divide equation 1 by 5:

{a+0 b = 2 | (equation 1)

{0 a+b = - 1 | (equation 2)

Collect results:

Answer: {a = 2

{b = - 1