Solve the system of equations by graphing: 2x + 3y = 2 6x + 18y = 9

A. (1/2, 1/3)

B. (2, 3)

C. (3, 2)

(4, 3)

(3, 4)

The answer is A: x=1/2, y = 1/3

Solve the following system:

{2 x + 3 y = 2 | (equation 1)

{6 x + 18 y = 9 | (equation 2)

Swap equation 1 with equation 2:

{6 x + 18 y = 9 | (equation 1)

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

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

{6 x + 18 y = 9 | (equation 1)

{0 x - 3 y = - 1 | (equation 2)

Divide equation 1 by 3:

{2 x + 6 y = 3 | (equation 1)

{0 x - 3 y = - 1 | (equation 2)

Multiply equation 2 by - 1:

{2 x + 6 y = 3 | (equation 1)

{0 x+3 y = 1 | (equation 2)

Divide equation 2 by 3:

{2 x + 6 y = 3 | (equation 1)

{0 x+y = 1/3 | (equation 2)

Subtract 6 * (equation 2) from equation 1:

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

v0 x+y = 1/3 | (equation 2)

Divide equation 1 by 2:

{x+0 y = 1/2 | (equation 1)

v0 x+y = 1/3 | (equation 2)

Collect results:

Answer: {x = 1/2, y = 1/3