What is the solution to the system of equations y=-1/3x+9 and y=2/3x+12

{x = - 3, y = 10

Step-by-step explanation:

Solve the following system:

{y = 9 - x/3 | (equation 1)

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

Express the system in standard form:

{x/3 + y = 9 | (equation 1)

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

Swap equation 1 with equation 2:

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

{x/3 + y = 9 | (equation 2)

Add 1/2 * (equation 1) to equation 2:

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

{0 x + (3 y) / 2 = 15 | (equation 2)

Multiply equation 1 by 3:

{ - (2 x) + 3 y = 36 | (equation 1)

{0 x + (3 y) / 2 = 15 | (equation 2)

Multiply equation 2 by 2/3:

{ - (2 x) + 3 y = 36 | (equation 1)

{0 x+y = 10 | (equation 2)

Subtract 3 * (equation 2) from equation 1:

{ - (2 x) + 0 y = 6 | (equation 1)

{0 x+y = 10 | (equation 2)

Divide equation 1 by - 2:

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

{0 x+y = 10 | (equation 2)

Collect results:

Answer: {x = - 3, y = 10