What is the solution of the system?

4x+3y=12

7x+5y=26

a. (18,20)

b. (18,-20)

c. (-20,18)

d. (20,18)

The Answer is b: x = 18, y = - 20

Proof:

Solve the following system:

{4 x + 3 y = 12 | (equation 1)

{7 x + 5 y = 26 | (equation 2)

Swap equation 1 with equation 2:

{7 x + 5 y = 26 | (equation 1)

{4 x + 3 y = 12 | (equation 2)

Subtract 4/7 * (equation 1) from equation 2:

{7 x + 5 y = 26 | (equation 1)

{0 x+y/7 = (-20) / 7 | (equation 2)

Multiply equation 2 by 7:

{7 x + 5 y = 26 | (equation 1)

{0 x+y = - 20 | (equation 2)

Subtract 5 * (equation 2) from equation 1:

{7 x+0 y = 126 | (equation 1)

{0 x+y = - 20 | (equation 2)

Divide equation 1 by 7:

{x+0 y = 18 | (equation 1)

{0 x+y = - 20 | (equation 2)

Collect results:

Answer: {x = 18, y = - 20