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:

{x = 18, y = -20

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