Question

3a + 4b = 2 5a + 9b =1

Answer 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