What is the solution system y=2/3x-2 y=-x+3

x = 3, y = 0

Step-by-step explanation:

Solve the following system:

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

y = 3 - x | (equation 2)

Express the system in standard form:

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

x + y = 3 | (equation 2)

Swap equation 1 with equation 2:

{x + y = 3 | (equation 1)

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

Add 2/3 * (equation 1) to equation 2:

{x + y = 3 | (equation 1)

0 x + (5 y) / 3 = 0 | (equation 2)

Multiply equation 2 by 3/5:

{x + y = 3 | (equation 1)

0 x+y = 0 | (equation 2)

Subtract equation 2 from equation 1:

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

0 x+y = 0 | (equation 2)

Collect results:

Answer: {x = 3, y = 0