3x - y = 12

4x - 5y = 16

x = 4, y = 0

Step-by-step explanation:

Solve the following system:

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

4 x - 5 y = 16 | (equation 2)

Swap equation 1 with equation 2:

{4 x - 5 y = 16 | (equation 1)

3 x - y = 12 | (equation 2)

Subtract 3/4 * (equation 1) from equation 2:

{4 x - 5 y = 16 | (equation 1)

0 x + (11 y) / 4 = 0 | (equation 2)

Multiply equation 2 by 4/11:

{4 x - 5 y = 16 | (equation 1)

0 x+y = 0 | (equation 2)

Add 5 * (equation 2) to equation 1:

{4 x+0 y = 16 | (equation 1)

0 x+y = 0 | (equation 2)

Divide equation 1 by 4:

{x+0 y = 4 | (equation 1)

0 x+y = 0 | (equation 2)

Collect results:

Answer: {x = 4, y = 0